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FORT DEARBORN HOTEL, CHICAGO 

Holabird & Roche, Architects 







STEEL CONSTRUCTION 


A TEXT AND REFERENCE BOOK COVERING 
THE DESIGN OF STEEL FRAME¬ 
WORK FOR BUILDINGS 


By HENRY JACKSON BURT, C.E. 

MEMBER AMERICAN SOCIETY OF CIVIL ENGINEERS 
MEMBER WESTERN SOCIETY OF ENGINEERS 
MEMBER SOCIETY FOR THE PROMOTION OF ENGINEERING EDUCATION 
STRUCTURAL ENGINEER FOR HOLABIRD AND ROCHE, ARCHITECTS 



ILLUSTRATED 


AMERICAN TECHNICAL SOCIETY 
CHICAGO 

1920 





COPYRIGHT, 1914, 1920, BY 
AMERICAN TECHNICAL SOCIETY 

COPYRIGHTED IN GREAT BRITAIN 
ALL RIGHTS RESERVED 



APR -9 i920 


©CU566462 



CONTENTS 


PAGE 

Introduction. 1 

Method of manufacture. 9 

Steel sections—adaptability and use. 23 

Properties of sections. 35 

General information. 40 

Quality of material. 42 

Standard specifications. 42 

Discussion of important features. 44 

Unit stresses. 49 

Rivets and bolts.:. 52 

Beams. 75 

Review of theory of beam design. 76 

Calculation of load effects. 80 

Calculation of resistance. 97 

Practical applications.113 

Details of construction.120 

Riveted girders. 134 

Theory of design. 135 

Design of plate girder.137 

Other forms of riveted girders. 158 

Practical applications.162 

Details of construction.165 

Compression members—columns.173 

Steel columns.173 

Loads and their effects.173 

Strength of columns—formulas.179 

Column sections.181 

Tables.188 

Details of construction.216 

Cast-iron columns.225 

Characteristics.225 

Strength—formula. 228 



































CONTENTS 


PAGE 


Compression members—columns 

Cast-iron columns 

Tables.230 

Details of construction.232 

Tension members.233 

Loads and their effects.233 

Sections.235 

Details of connections.237 

Wind bracing.239 

General conditions.239 

Systems of framework.243 

Design of wind-bracing girders..255 

Combined wind and gravity stresses in girders.2G2 

Effect of wind stresses on columns. 2GG 

Practical design—a sixteen-story fireproof hotel.2G9 

Fireproof specifications.294 

Loads.295 

Type of floor construction.301 

Framing specifications.306 

Design of steel members.309 

Column pedestals.319 

Wind bracing.322 

Miscellaneous features.327 

Dimensioning drawings. 329 

Protection of steel. 333 

Protection from rust.333 

Rust formation.333 

Paint. 335 

Protection from fire.339 

Specifications .... . 349 

General characteristics.:.350 

Example of specifications.353 


Index 


373 


































INTRODUCTION 


% 

A GREAT part of the satisfaction derived from the practice 
of engineering comes from seeing the “dreams come true”. 
The engineer is commonly assumed to deal with facts and to be 
guided by mathematical relations. While this is true, he must at 
times be a dreamer, a man with an active imagination. Before a line 
is drawn or a figure placed on paper, the engineer must have some 
conception of the structure he is to create. The more definite 
» this conception, the more readily it can be committed to paper 
in the form of drawings. The mention of a building of a certain 
size or for a certain purpose brings a vision of the skeleton to 
support it; the architect’s perspective or elevation suggests the 
columns concealed within the piers and the girders behind the 
spandrels; the floor plans indicate the location of columns, girders, 
and joists which will be required to support the floors, partitions, 
and walls. From these mental pictures, the design drawings 
can be evolved by applying the mathematical relations to deter¬ 
mine the sizes of members required. 

<1 But the use of the imagination does not stop here; it is needed 
in perfecting the details. The more fully it # is developed, the 
more quickly can proper sizes and arrangement of material be 
established. Imagination is a natural talent which can be im¬ 
proved by practice and experience. It is not easily distinguished 
from the judgment resulting from experience. 

This book does not deal with the visions of proposed struc¬ 
tures, but with the facts and formulas for transforming these 
visions into tangible designs. Haying realized the dream in 
definite plans, there follows the growth of the practicable struc¬ 
ture. The successful completion of the skeleton which, silently 


INTRODUCTION 


and unseen, must carry the weight of the building with assurance 
of perfect safety to the people who occupy it, must give great 
satisfaction to him whose brain has created it. Then has the 
“dream come true”. 

<1 This book is intended to give its students the facts and formulas 
needed in designing the structural steel framework for buildings. 
Since facts and formulas alone would be of little use, they are 
accompanied by explanations of the underlying principles, a 
clear understanding of which is essential to the intelligent use 
of the formulas. The use of the formulas is shown by illus¬ 
trations of a practical nature which serve not only to teach the 
proper application, but to illustrate current practice in this form 
of construction. 

<1 For use as a textbook by students, the important feature is 
the theory on which are based the formulas and their applications. 
A student can easily learn to use tables, apply formulas, and copy 
the work of others. But without a knowledge of the fundamental 
principles he will not be able to determine the proper limitations 
of the tables and formulas nor to distinguish the good and bad 
features of designs made by himself or others. 

<1 For use as a reference by designers, the book brings together 
the necessary data, easily accessible, for the complete design of 
structural steel work for business buildings, and gives enough 
illustrations to guide in the solution of the problems usually 
encountered in practice. A unique feature of this book is a 
complete set of drawings and detailed explanations in connection 
with the design of a sixteen-story hotel. This study alone cannot 
help but be of immense benefit to those who are interested in 
the design end of this most important subject. 



UNIVERSITY CLUB, CHICAGO 
Holabird & Roche, Architects 
























MONROE BUILDING, CHICAGO 
Holabird & Roche, Architects 








STEEL CONSTRUCTION 


PART I * 

INTRODUCTION 

Scope of Work. The subject of steel construction as here used 
covers the use of structural steel for the supports for buildings, 
whether in the forms of isolated members or complete framework. 
It deals especially with architectural structures, such as business 
buildings, office buildings, warehouses, residences, etc. Mill build¬ 
ings and roof trusses might properly be included Under this subject, 
but as they are not absolutely essential to the present discussion, 
their treatment has been omitted. 

Consideration is given first to the structural steel sections, i. e., 
the shapes in which the material is available, such as plates, angles, 
I-beams, etc., studying their properties and uses. Certain definite 
sizes, shapes, and weights of sections can be purchased in the mar¬ 
ket. Acquaintance with these sections and some knowledge of the 
purposes for which the special shapes are adapted are essential 
preliminaries to the study of steel design. 

The designer should know the quality of the material which he 
is using; therefore, a brief discussion of the chemical composition 
and physical properties of steel for structural purposes is given. 

Experience and experiment have established the working loads, 
i. e., unit stresses, that can be applied safely to structural steel under 
various conditions. The values now used are so well established 
that they may be considered as standard. Consequently, the unit 
stresses are given with only such discussion as is necessary to explain 
their application. 

After these preliminary considerations comes the study of 
design. As rivets and bolts are used in all forms of structural 
members, a section of the text is devoted to them before taking up 
beams, columns, and tension members. The study of these mem- 



2 


STEEL CONSTRUCTION 


bers gives a review of the theory involved, the formulas, the compu¬ 
tation of loads, the application to assumed cases, and details of 
construction. 

Having studied the elements of the structure as described 
above, complete structures are then investigated and designed. 
Examples of existing structures are taken for this purpose. And, 
finally, there is a discussion of painting, fireproofing, and speci¬ 
fications. 

Structural steel is a perishable material if exposed to the ele¬ 
ments and is so to a considerable extent when enclosed in a building 
but exposed freely to the air. It is a dangerous material when 
exposed to fire. A part of the designer’s duty is to provide the 
necessary protection from corrosion and from fire; consequently, 
considerable attention is given to painting and fireproofing. 

The specifications for structural steel are quite well standard¬ 
ized so far as usual provisions are concerned. Nevertheless, some 
modifications or additions are usually required for each job. The 
requirements are outlined briefly in the text. 

Purpose. It is the purpose of this book to give a thorough 
presentation of the theory and practice of design. It is believed 
that careful study of the text and faithful work in solving the prob¬ 
lems will furnish the proper equipment for designing any ordinary 
steel construction. The ability to deal with complicated problems 
will follow naturally after practice with the simpler ones. 

In addition to its uses as a textbook, this work is suitable for a 
reference book for designers, being especially useful to those who 
have to design steel w r ork only occasionally, and to beginners in 
practical work. It does not pretend to offer anything new, but 
aims to explain in a simple Way the established theory and 
practice. 

Preparation. Fundamental Principles. In order to take up 
the design of structural steel work, it is necessary that one have an 
understanding of the theory and the formulas used in the design 
of the steel members. It is assumed that the essential parts of the 
theory, as referred to in “Strength of Materials”, “Structural 
Drafting”, “Statics”, and “Roof Trusses”, have been mastered, 
and if this is not true, these subjects should be reviewed before 
proceeding with “Steel Construction”. 


STEEL CONSTRUCTION 


3 


It is of the greatest importance that the fundamental principles, 
that is, the theory underlying the operations in designing, be kept 
in mind. Only in this way can one be sure that no step in the work 
has been omitted. This understanding of the theory will, in a large 
measure, remove the necessity for formulas. It would be impossible 
to illustrate all the problems that come up in actual practice, so that 
the designer must understand the theory in order to design with 
reasonable assurance of correctness and to solve the innumerable 
problems that arise. 

Simple Mathematical Requirements. The mathematics required, 
in designing are little more than arithmetic. It is true that the', 
formulas are expressed in algebraic terms, but as these formulas 
are in the form required for direct application to the problems, no 
algebraic transformations are 
necessary in ordinary cases. The 
w r ork to be done simply consists 
in substituting numerical values 
for the letters and performing 
the additions, subtractions, mul¬ 
tiplications, and divisions indi¬ 
cated by the symbols. The 
formulas will be stated in words 
as well as in letters so that the 
designer need not follow set 
examples. 

Equilibrium Relations. The 
three fundamental relations of equilibrium, illustrated in Fig. 1, 
must always be kept in mind, viz: 

(1) Summation of horizontal forces equals zero 

(2) Summation of vertical forces equals zero 

(3) Summation of moments equals zero 

In the textbook on “Statics,” equilibrium is defined as follows: 
When a number of forces act upon a body which is at rest, each tends 
to move it; but the effects of all the forces acting upon that body may 
counteract or neutralize one another, and the forces are said to be bal¬ 
anced or in equilibrium. 

Fig. 1-a represents a body to which certain forces are applied. 
The horizontal forces h and h' are equal and opposite in direction, 




i/ - 500 


h « IO00 



h'-IOOO 





la) 

v'^500 




Fig. 1. Diagram Showing Forces in 
Equilibrium 

















4 


STEEL CONSTRUCTION 


thus satisfying the first relation. Likewise the vertical forces satisfy 
the second relation. The horizontal forces are in the same straight 
line and the vertical forces are in one straight line, hence there is 
no tendency to rotate and the third relation is satisfied. All of this 
is evident from the drawing. 

Fig. 1-b represents a more complicated case. There are no 
horizontal forces. The vertical forces acting downward are 1000 
+500 = 1500; acting upward are 850+650=1500; hence the sum¬ 
mation equals zero. Taking any point o as a center, the moments 
clockwise are 

5X1000 = 5000 
9X 500 = 4500 

9500 

The moments in the opposite direction are 

2X 850 = 1700 
12X 650 = 7800 

9500 

Hence the summation of moments equals zero, and the forces 
acting on the body are in equilibrium. 

It is because it is essential that these relations be mastered 
that they are stated here. They will be referred to frequently 
throughout the work on designing. 

Method of Presentation. Throughout the discussion relating to 
the design of structural steel members, the order of presentation is 

(a) Review of Theory 

(b) Calculation of Loads 

(c) Calculation of Resistance 

(d) Practical Application 

(e) Details of Construction 

Review of Theory. Although it has been assumed that the 
student has had some training in the theory of design, this subject 
is briefly reviewed. 

Calculation of Loads. The calculation of loads on steel mem¬ 
bers is usually the most laborious part of designing. This work has 
to be done in each individual case, as it is not possible to standard¬ 
ize the loads which are applied to structures. Accurate data as to 
the weights of the materials of construction which must be sup- 




STEEL CONSTRUCTION 


5 


ported by the steel framework are not always available; in fact, 
the weights of certain materials, as furnished by different manu¬ 
facturers, vary considerably. The live, or imposed, loads must 
generally be assumed or approximated from prospective conditions 
of use which may be more or less uncertain. Consequently, this 
branch of the study involves not only careful computation, but the 
exercise of judgment 

Calculation of Resistance. The calculation of resistance of steel 
members to the loads applied is also a laborious matter when a start 
must be made from the beginning, but the steel construction has 
been so standardized that the number of sizes of material used is 
relatively small. Tables are available, giving the properties and 
resistance factors of these sections, so that it is usually an easy 
matter to design the section required for a given situation after the 
loads have been computed. This statement does not apply very 
generally to built-up sections such as plate girders and columns, as 
these members have been standardized only to a limited extent. 
Consequently, it is necessary for the designer to be able to compute 
the resistance of the member, having given only its dimensions and 
the permissible unit loads. Even in the case of I-beams there are 
many cases where the work must go back to the fundamental rela¬ 
tions; as, for example, in cases where holes are punched in the 
tension flange of a beam at the point of maximum bending moment, 
or where a portion of the flange is cut away 

Practical Application. Numerous examples are worked out to 
illustrate the principles and methods covered by the text, and 
similar problems are submitted for solution. The Examples and 
problems are taken from actual construction work, as it is believed 
that they are more useful and interesting than abstract illustrations. 

Details of Construction. This section of the work explains the 
usual methods used in detailing the connections of steel members 
to each other and is illustrated by numerous drawings. 

Reference Books. Tables giving the properties of steel sec¬ 
tions and data giving the strength of steel members are given in the 
handbooks published by the steel manufacturers. These books are 
so convenient for reference and so easily obtainable that no attempt 
is made to repeat in this text the tables and data given in them, the 
supposition being that the reader either has one or will provide 


6 


STEEL CONSTRUCTION 


himself with one of these handbooks. References are repeatedly 
made to the handbooks and, as far as practicable, are made in 
general terms, so that any one of the reference books may be used. 
This is an important point, as these reference books are being revised 
from time to time and the one in use at the present time might 
be supplanted in a year or two by one of another manufacturer 
which is more up-to-date. Handbooks are published by The Cam¬ 
bria Steel Company, Johnstown, Pa.; Carnegie Steel Company, 
Pittsburgh, Pa.; Jones and Laughlins, Pittsburgh, Pa.; and Bethle¬ 
hem Steel Company, South Bethlehem, Pa. 

In addition to the handbooks there are a number of other 
reference books available for special purposes that can be purchased 
through the book stores. They are not essential for this study, but 
are of considerable use to designers. They will be referred to in 
the text in connection with the special features to which they relate. 

Tables. The tables given in reference books are generally 
reliable; nevertheless, errors do occur in them and it is prudent to 
check them with the formulas sufficiently to make sure that they 
are computed on a correct basis, or that the user understands the 
basis on which they are computed. As an illustration of the latter 
point, attention is called to the fact that some tables of strength 
are stated in tons and others in thousands of pounds. Of course the 
heading of the table should show this, but special care should be 
taken to make sure which is used. A designer may be using a table 
for beams given in tons and a table for columns given in thousands of 
pounds, in which case it would be very easy to get columns designed 
only half strong enough or beams with tw r ice the necessary strength. 
Similarly, there is a chance for confusion between moments expressed 
in foot-pounds and moments expressed in inch-pounds. Also there 
is a chance for error in using the weight per lineal foot of a section 
when it is intended to use the cross-sectional area, or vice versa • 
This matter is given further consideration later. 

Problem 

Refer to the handbook and make a list of all the tables therein in 
which the strength is given in tons, and another list in which the strength is 
given in pounds or .thousands of pounds. 

If the handbook has been well edited, all tables will have- the 
same basis. Make a careful search of the book to ascertain definitely 


STEEL CONSTRUCTION 


7 


its make-up in this relation. When there is occasion to use a 
different handbook, investigate immediately in the same manner. 
Pboblem 

Refer to the handbook for all references and tables relating to moments. 
Make a list of all cases where moments are expressed in foot-pounds and another 
list of cases where they are expressed in inch-pounds. 

Note that moments of inertia are always expressed in inches, 
so that in all cases where the moments of inertia of sections are used 
in computations, the bending moment must be expressed in inch- 
pounds. On the other hand, the resisting moments of beams are 
usually given in foot-pounds, and the bending moments must be 
computed in the.same units 
Problem 

Select at random from the handbook twenty or more different sizes of 
angles, I-beams, plates, etc., and set down in parallel columns the area in square 
inches and the weight per lineal foot of each item. 

Note that in each case the weight is 3.4 times the area. That 
is, a piece of steel having a cross-sectional area of one square inch 
weighs 3.4 pounds per lineal foot. 

Problem 

What is the weight of one cubic foot of steel? Of one cubic inch of steel?. 

Factor of Safety. Older works and specifications dealing with 
steel construction frequently use the expression “factor of safety.” 
It is used to express the ratio of the ultimate strength of the material 
to the safe working strength. In steel construction, this ratio is 
commonly stated to be^ 4, being based on the ultimate strength of 
64,000 pounds per square inch and a working strength of 16,000 
pounds per square inch. This expression is a misnomer and its use 
is to be discouraged, because it gives a wrong understanding of the 
facts and leads to an unwarranted sense of security. Later on in 
this treatise it is shown that the actual strength of steel work under 
loads continuously applied is only about one-half of the ultimate 
strength of the material, so that the real factor of safety is 2 where 
the nominal factor of safety is 4 

Further this expression has been used unscrupulously in argu¬ 
ments with owners to persuade them to use lighter steel work than 
standard practice permits; and, on the other hand, it has been used 
by the owners themselves without realizing the true meaning of 
the expression, in an attempt to reduce cost. 


8 


STEEL CONSTRUCTION 


This expression is quite certain to come up from time to time 
in discussions with laymen and in such cases the distinction between 
the actual and the nominal factors of safety must be made clear. 

Procedure in Furnishing Structural Steel. There are three 
steps in furnishing structural steel: first, the rolling of the plain 
material; second, the fabrication of the plain material into the con¬ 
ditions required for use; and third, the erection of the material in the 
structure. 

The work of the rolling mill consists in rolling the steel sec¬ 
tions of the sizes and lengths as required by the order. The 
work of the fabricating shop is to do the punching, cutting, assem¬ 
bling, riveting, and painting of the material as required for use jn the 
structure. The work of the erector is to place the pieces in position 
in the structure and bolt or rivet them together. Some concerns 
perform all three of these steps; many perform only the second and 
third; and in still other cases the second and third steps may be 
performed by separate organizations. The owner may deal with a 
general contractor who undertakes to secure the performance of all 
three steps; or he may deal separately with a fabricating company 
and with an erection company. The former undertakes to deliver the 
fabricated material ready for erection, purchasing the material from 
the rolling mills. It is only in very rare instances that separate con¬ 
tracts are made for furnishing the plain material and for fabricating. 

The design of the structural steel work is usually made by an 
architect, or by an engineer co-operating with the architect. The 
design drawings should show all the necessary dimensions of the 
structure, sizes of members, loads on the individual members, and 
details of connections other than those considered as standard. 
These drawings show the members assembled in their proper rela¬ 
tions to each other. They must also show any connections required 
for attaching or supporting other construction materials. 

As a part of the work of fabricating, working drawings must be 
prepared by the engineering department of the fabricating com¬ 
pany, or by other engineers employed by it. These working draw¬ 
ings, or shop details, divide the work into individual members, and 
a complete drawing is made of each member, showing all dimen¬ 
sions, the position of rivets, and the exact location of the open holes 
required for connections with other members of the structure. 


STEEL CONSTRUCTION 


9 


STRUCTURAL STEEL 

METHODS OF MANUFACTURE 

The procedure in the manufacture of structural steel sections 
from iron ore consists of the following operations: (1) smelting the 
iron ore and producing pig iron; (2) converting the pig iron into 
steel ingots; and (3) rolling the ingots into steel sections. 

Iron Ore to Pig Iron. Iron ore is a chemical combination of 
iron and oxygen. It exists in several forms. Pure ore has a maxi¬ 
mum of about 70 per cent of iron. The ores as mined are mixed 
with various substances, chiefly water, silica, and limestone, with 
small quantities of phosphorus, sulphur, titanium, manganese, etc., 
so that commercial ore contains only 50 per cent of iron, or even 
less. 

Process of Smelting.' The purpose of smelting the ore is to 
break down the chemical combination of iron and oxygen, and to 
eliminate the greater part of the impurities from the resulting 
metallic iron. This is accomplished by melting the ore in a blast 
furnace The heat for melting the ore is supplied by coke, and 
the melting point is brought to a lower temperature than otherwise 
would be required by mixing limestone with the ore. As the con¬ 
tents of the furnace melt, they drip down to the bottom where the 
molten iron separates from the molten slag by gravity, the iron, 
being heavier, settling to the bottom. 

A section of a blast furnace and skip hoist is shown in Fig. 2. 
The skip or car at the bottom of the machine is loaded with ore, 
limestone, and coke from the bins; it is then hauled up the incline 
where the material is charged into the blast furnace. Fig. 3 shows 
a section through the bottom part of the furnace, which represents 
graphically the melting charge and the accumulation of iron 
and slag in separate layers at the bottom of the furnace. The blast 
of air required for burning the coke is admitted through the open¬ 
ings, called “tuyeres,” near the bottom of the furnace. 

The operation of the blast furnace is continuous from the time 
it is fired until it is shut down for repairs, or for other reasons. As 
the metal and slag accumulate at the bottom, they are drawn off, 
the metal into molds to form pigs, Fig. 4, and the slag to the dump. 
More material is added at the top of the furnace as the contents melt. 


10 


STEEL CONSTRUCTION 


Pig Iron. The pig iron resulting from this operation contains 
3 or 4 per cent of carbon; a small amount of sulphur which has been 
absorbed from the coke; about 4 per cent of silicon; and smaller 
quantities of manganese and phosphorus which remain from the ore. 



The iron may not be cast into pigs but may be maintained in 
a molten condition ready for the next operation, if the Bessemer 
process is used. In this case it is poured into a large vessel, called 















































































































































































STEEL CONSTRUCTION 


11 



a “mixer,” Fig. 5, which may hold as much as 500 tons. Heat can 
be applied to it if needed. 

Pig Iron to Steel. The change from pig iron to steel consists 
of the reduction of the carbon to about 0.2 per cent and the elimina- 


Legend i — Lumps of Coke_ 

Lumps of Iron Ore_ 

Lumps of Lime_O 

Drops of Slag_ i 

Drops of Iron_/ 

Layer of Molten Slag_ 

Layer of Molten Iron_=—§5=3 

Fig. 3. Section Through Base of Furnace Showing Layers of Molten Iron and 
■' ’ Slag with Unmelted Ingredients Above 

From Stoughton’s “Metallurgy of Iron and Steel 
Courtesy McGraw-Hill Publishing Company 

tion of impurities as fully as possible. There are two processes of 
doing this, the Bessemer and the Open Hearth. They are described 
in “Metallurgy of Iron and Steel”* as follows: 

*By Bradley Stoughton, Copyright 1913, McGraw-Hill Riblishing Company. 
































































Fig. 4. Pig Beds 

From Stoughton’s “Metallurgy of Iron and Steel” 
Courtesy, McGraw-Hill Publishing Company 



















STEEL CONSTRUCTION 


13 


“Bessemer Process. In the Bessemer process, perhaps 10 tons of 
melted pig iron are poured into a hollow pear-shaped converter, 
Figs. 5,6 and 7, lined with silicious material. Through the molten 



Fig. 5. Section Through a Mixer 
From Stoughton's “Metallurgy of Iron and Steel’’ 
Courtesy, McGraw-Hill Publishing Company 


material is then forced 25,000 cubic feet of cold air per minute. In 
about four minutes the silicon and manganese are all oxidized by 
the oxygen of the air and have formed a slag. The carbon then 
begins to oxidize to carbon monoxide, CO, and this boils up through 
the metal and pours out of the mouth of the vessel in a long brilliant 
flame, Fig. 8. After another six minutes, the flame shortens or 
‘drops’; the operator now knows that the carbon has been eliminated 
to the lowest practicable limit, say 0.04 per cent, and the operation 
is stopped. 'So great has been the heat evolved by the oxidation of 
the impurities that the temperature is now higher than it was at 
the start, and we have a white-hot 
liquid mass of relatively pure metal. 

To this is added a carefully calculated 
amount of carbon to produce the de¬ 
sired degree of strength or hardness, 

or both; also about 1.5 per cent of _ 

manganese and 0.2 per cent of' silicon. 5h o^ldlr 
The manganese is added -do remove 

from the bath the oxygen with which Fig. 6. Parts of Converter 
it has become charged during the ope- Courtesy McGraw-H ill Publishing Company 


BACK 








































14 


STEEL CONSTRUCTION 


ration and which would render the steel unfit for use. The silicon 
is added to get rid of the gases which are contained in the bath. 
After adding these materials, or “recarburizing” as it is called, the 
metal is poured into ingots which are allowed to solidify, and then 
rolled, while hot, into the desired sizes and forms. The character¬ 
istics of the Bessemer process are: (a) great rapidity of purification, 
say tf;'> minutes per “heat”; (b) no extraneous fuel is used; and 



Fig- 7. Section Through Bessemer Converter While Blowing 
From Stoughton’s “Metallurgy of Iron and Steel” 
Courtesy McGraw-Hill Publishing Company 


(c) the metal is not melted in the furnace where the purification 
takes place. 

“Acid. Opcn-IIearth Process. The acid open-hearth furnace is 
heated by burning within it gas and air, each of which has been 
highly preheated before it enters the combustion chamber. A sec¬ 
tion of the furnace is shown in Fig. 9. The metal lies in a shallow 
pool on the long hearth, composed of silicious material, and is 





























































































STEEL CONSTRUCTION 


15 


heated by radiation from the intense flame produced as described. 
The impurities are oxidized by an excess of oxygen in the furnace 
gases over that necessary to burn the gas. This action is so slow, 
however, that the 3 to 4 per cent of carbon in the pig iron takes a 



Fig. 8 A Bessemer Blow 
From Stoughton’s "‘Metallurgy of Iron and Steel” 
Courtesy McGraw-Hill Publishing Company 


long time for combustion. The operation is therefore hastened in 
two ways: (a) iron ore is added to the bath, and (b) the carbon is 
diluted by adding varying amounts of cold steel scrap. The steel 















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5mS 


nnriianrinnr 


laansonaE; 


innannrinr 


Chimney Flue 






16 STEEL CONSTRUCTION 


add to the bath a sufficient amount of lime to form a very basic 
slag. This slag will dissolve all the phosphorus that is oxidized, 
which an acid slag will not do. We can oxidize the phosphorus in 
any of these processes, but in the acid Bessemer and the acid open- 
hearth furnaces the highly silicious slag rejects the phosphorus, and 
it is immediately deoxidized again and returns to the iron. The 
characteristics of the basic- open-hearth process are the same as 
those of the acid open-hearth with the addition of: (e) lime added to 


scrap is added to the furnace charge at the beginning of the process, 
and it takes from 6 to 10 hours to purify a charge, after which 
we recarburize and cast the metal into ingots. The characteristics 
of the open-hearth process are: (a) long time occupied in purifica¬ 
tion ; (b) large charges treated in the furnace (modern practice is 
usually 30 to 70 tons to a furnace); (c) at least part of the charge 
melted in the purification furnace; and (d) furnace heated with 
preheated gas and air, Fig. 10. 

“Basic Open-Hearth Process. The basic open-hearth operation 
is similar to the acid open-hearth process, with the difference that we 


Air 

Fig. 9. Section of Regenerative Open-Hearth Furnace 

From Stoughton's “Metallurgy of Iron and Steel” 
Courtesy McGraw-Hill Publishing Company 














































































































































































































































































































































































18 


STEEL CONSTRUCTION 


produce a basic slag; (f) hearth lined with basic, instead of silicious, 
material, in order that it may not be eaten away by this slag; and 
(g) impure iron and scrap may be used, because phosphorus, and, 
to a limited extent, sulphur can be removed in the operation.” 


Rolling the Ingots. The steel in the ingot is in its final condi¬ 
tion as to chemical composition, Figs. 11 and 12, and must now be 



Fig. 11. Steel Ingots Incased in the Molds and Resting on Car 
From Stoughton’s Metallurgy of Iron and Stee 
Courtesy McGraw-Hill Publishing Company 


worked into the shapes required for structural uses. This is done 
by passing the steel between rolls. 

Rolls are used in pairs, called a “two-high mill”, as shown in 
Fig. 13, or in sets of three, called a “three-high mill”, as shown in 
Fig. 14. As the piece goes through the same mill several times, the 
two-high mill must be reversed for each pass or else the piece must 
be taken over or around the mill between the successive passes. 
These disadvantages are eliminated by the use of the three-high 









STEEL CONSTRUCTION 


19 




mill, in which the rolls rotate continuously and work is done on the 
piece as it passes back and forth. 

Blooming. Before going to 
the rolls, the ingot is placed in a 
furnace, called the “soaking pit’’, 
in which it is heated to a high 
temperature. In passing between 
the rolls, Fig. 13, a heavy pres¬ 
sure is exerted on the metal, 
which reduces it in thickness, in¬ 
creases it in width to some ex¬ 
tent, and extends it greatly in 
length. If the material is des¬ 
tined to be made into plates, it 
is rolled into a slab in the first 
set of rolls; if it is for structural 
shapes, the ingot will be turned 
alternately from side to edge in 
passing through the rolls so that 
it will be kept approximately scpiare in section until it is reduced 
to the proper size for beginning to form the shape. At this stage 
it is called a “bloom” and the 
rolls are called “blooming rolls”, 

Fig. 15. 


Fig. 12. Stripping the Ingots 
Courtesy McGraw-Hill Publishing Company 



Fig. 13. Action on Steel in '“Two-High” Mill Fig. 14. Action on Steel in “Three-High” Mill 
Courtesy McGraw-Hill Publishing Company Courtesy McGraw-Hill Publishing Company 


Boughing and Finishing Rolls. The next step is to pass the 
steel through the roughing rolls. These rolls are grooved in such 



20 


STEEL CONSTRUCTION 



I*ig I.j. “Two-High" Blooming Rolls 
Courtesy Svatnan. IS led h Company 


a way that the successive passes gradually develop the metal toward 
the required shape. Finally it goes through the finishing rolls 
which bring the section to the required shape and size. This process 
is clearly illustrated by Figs. *16, 17, 18, 19, and 20. 



Fig. 16. “Three-High” I-Beam Roughing Rolls 
Courtesy Seaman, Sleeth Company 


♦Catalogue of Phoenix Roll Works, by permission. 








STEEL CONSTRUCTION 


21 




I'ig. 17 ‘Three-High” I-Beam Finishing Rolls 
Courtesy Seaman, Sleeth Company 


Fig. 18. “Three-High” Equal Angle Roughing 
Courtesy Seaman, Sleeth Company 










Plate Rolls. A three-high set of plate rolls is shown in Fig. 
21. There is nothing to control the width of the plates, therefore 
the edges *of plates rolled in this mill will be uneven and must be 
sheared to the correct width after the rolling is completed. Such 
plates are known as “sheared plates.” 

Vertical rolls can be placed in front of the horizontal rolls to 






22 STEEL CONSTRUCTION 


Fig. 19. “Three-High” Equal Angle Finishing Rolls 
Courtesy Seaman, Sleeth Company 


Fig. 20. “Three-High” Z-Bar Rolls 
Courtesy Seaman, Sleeth Company 







STEEL CONSTRUCTION 


23 


control the width, as shown in the left-hand view, Fig. 22. Such a 
mill is called a “Universal Mill” and the plates produced by it are 



Fig. 21. “Three-High” Chill Plate Rolls 
Courtesy Seaman, Sleeth Company 


called “Universal Mill plates,” or edged plates. Fig. 22 is a special 
form known as the Grey mill and is used by the Bethlehem Steel 
Company for making I-beams and column sections. Fig. 23 is a 
3-high Universal Mill manufactured by the United Engineering and 
Foundry Company, Pittsburgh. 



Fig. 22. Universal Mill for Rolling Bethlehem Beams 


STEEL SECTIONS—ADAPTABILITY AND USE 

Classification of Sections. Structural steel members are gener¬ 
ally designated by the shapes of their cross sections. Thus a member 
whose cross section has the shape of a capital letter I is called an 
I-beam. The other important sections are channels, angles, zees, 
















































Fig. 23. 48-Inch "Three High” Universal Mill 
Courtesy United Engineering <£- Foundry Company 



















STEEL CONSTRUCTION 


25 


tees, and H-sections, whose shapes are indicated by the names. 
Round and square members are called “rods” and “bars”. Flat 
members six inches wide and less are usually designated as “bars” 
or “flats”. Flat members wider than six inches are designated as 
“plates”. Structural sections are frequently designated as “plates” 
and “shapes”. In general, the structural shapes are standard. 

Standard Sections. The shapes in common use conform to the 
standards of the Association of American Steel Manufacturers. 
These standard shapes as made by the various manufacturers are 
identical in dimensions and weights; therefore, in designing it is 
only necessary to specify the sections and not the name of the 
manufacturer. 

Special Sections. In addition to the standard sections, most 
manufacturers make some special sections. Some of these are now 
so common that they are as available as standard sections, but 
generally it is advisable for the designer to give the name of the manu¬ 
facturer in specifying them. The handbooks indicate which sections 
are standard and which are special.* The designer should generally 
use only standard sections. This matter 
is given full consideration elsewhere in 
this text. Use the handbook for con¬ 
stant reference in the following discussion 
of the sections. 

I-Beams. Standard Sections. An 
I-beam, Fig. 24, is designated by the 
depth and the weight per lineal foot,thus: 

12" I 31*# 

The standard depths are 3, 4, 5, 6, 7, 8, 

9, 10, 12, 15, 18, 20, and 24 inches, respectively. For each depth 
there are several standard weights. Most of the mills also make 
some special weights, viz: 

12" deep weighing 40 to 55# 

15" deep weighing 60 to 80# 

15" deep weighing 80 to 100# 

20" deep weighing 80 to 100# 

♦The 1903 edition of the “Carnegie Handbook” used the term standard in relation, to beams 
and channels to apply to the minimum weight of each size. It is preferable to limit the use of 
the term to the sections adopted by the Association of American Steel Manufacturers. 


r LANGE 



or rLANGE 

Fig. 24. Details of Standard 
I-Beam Section 














26 


STEEL CONSTRUCTION 


Carnegie Sections. The Carnegie Steel Company rolls some 
additional sizes of special beams which are similar to the standard 
beams, as follows: 

24" deep weighing 105 to 115# 

18" deep weighing 75 td 100# 

It also rolls special sizes of certain depths which are lighter than the 
minimum weight standard beams. They are as follows: 

*10" I 22# 18" I 46# 

12" I 27^# 21" I 57£# 

15" I 36# 24" I G9§# 

27" I 83# 


A distinctive feature of these beams is that the fillets connecting 
flange to web form a compound curve instead of a simple curvfc as 
in the standard beams. 

Bethlehem Sections. The Bethlehem Steel Company! makes a 
series of special I-beams ranging in depth from 8 to 30 inches. 

The minimum weights of these beams are about 
10 per cent less than the minimum weights of 
the corresponding standard beams. The section 
is so designed that the theoretical strength of 
the minimum section is about the same as that 
of the standard section. This is accomplished 
by putting less metal in the web and more in 
the flanges. Fig. 25 gives the dimensions of 
the Bethlehem 15" I 38#. Comparison with 
the corresponding standard beam shows: 



■RADIUS.3&‘ 


cial Section 15’ I 38^ 


Web thickness 
Flange width 
Moment of inertia 


15" I 38# 
.29" 
6 . 66 " 
442.60 


15" I 42# 
.41" 
5.50" 
441.80 


The Bethlehem Company also makes a series of girder beams 
ranging in depth from 8 to 30 inches. These beams are much 


♦Apply to the nearest office of the Carnegie Steel Company or the Illinois Steel Company, 
for a circular giving the properties of these beams, or see "Pocket Companion,” Carnegie Steel 
Company, 1913. 

t Complete data are 'given in the'Company’s handbook. 










STEEL CONSTRUCTION 


27 




. 44 " 


heavier than either the standard beams or the Bethlehem special 
beams and the flanges are also much wider. Fig. 26 gives the 
dimensions of the Bethlehem girder 15"X73#. 

Efficiency of Minimum Sections. Note in the handbook that 
the weights of beams of a given depth 
are grouped. The beams in a group 
are rolled with the same rolls, the min¬ 
imum section being produced when the 
rolls are set close together, and the 
heavier sections being made by spread¬ 
ing the rolls. In this change the depth 
remains constant, while the web is thick¬ 
ened and the flanges widened. In Fig. 

27, the shaded portion represents the Fig - 26 - Bethlehem Girder i5'x73# 

minimum section, and the unshaded portion represents the metal 
added to produce the heavier section. From this it is clear that most 
of the added metal is in the web, and is not placed to such good advan¬ 
tage as the metal in the minimum section. The increased strength 
is not nearly so great as the increased weight. For example, 
compare 15" I 42# with 15" I 60# of the same group. The increase 

18 

in weight is 18 pounds, or — = 43%. The increase in strength 




Fig. 27. Showing 
Method of In¬ 
creasing Section 
of I-Beams 


as indicated by the change in the moment of iner¬ 
tia from 441.8 to 538.6 is 96.8, or - ?jy*- =22%. 

441.8 

Thus it appears that the minimum weight of each 
group is the most efficient. As a consequence the 
range in weight from a given set of rolls is limited to 
about 20 pounds. When a greater range is required 
for a given depth of beam, more than one set of 
rolls is used. Now compare the standard 15" I 60# 
and the special 15" I 60#. Their respective mo¬ 
ments of inertia are 538.6 and 609.0. The differ¬ 


ence is 70.4, or ^t = 13%. This illustrates the advantage of 

538.6 

having the additional set of rolls. More than one set of rolls 
is provided for 12-inch, 15-inch, 18-inch, 20-inch and 24-inch 
beams. 


















28 


STEEL CONSTRUCTION 


Problem 

Make full-size drawings on tracing paper of the following sections: 


Standard 

15" 

I 42# 

Standard 

15" 

I 55# 

Special 

15" 

I 60# 

Special 

15" 

I 80# 

Special 

15" 

I 100# 

Carnegie 

15" 

I 36# 

Bethlehem 

15" 

I 38# 

Bethlehem 

15" 

GB 73# 


Superimpose these tracings and note the difference in thickness of web, width of 
flange, and shape of fillets. 


Characteristics and Uses. An inspection of an I-beam section 
shows it is much stiffer in one direction than in the other. The section 
is designed to resist bending in one direction only, i. e., in the plane 
of the web of the beam. The I-beam is used almost exclusively for 

this purpose, though to a limited extent it is 
used in built-up columns. When used in a 
column, it is economical only when com¬ 
bined with other sections to give stiffness in 
both directions. It is sometimes used alone 
as a column when the limitations of space 
offset the lack of economy in weight. 

Beams less than 6 inches deep are not 
often used in the framework for buildings. 
On many jobs the minimum is 8 inches. 

Channels. Standard'and Special Sections. A channel, Fig. 28, 
is designated by the depth and the weight per lineal foot, thus: 



Section 


15" E33# 


The standard depths are 3, 4, 5, 6, 7, 8, 9, 10, 12, and 15 inches, 
respectively. For each depth there are several weights. A number 
of special sizes and weights are made but they are not much used 
for structural purposes. The Cambria Steel Company makes a 
group of channels 18 inches deep, weighing from 45 to 60 pounds. 

The weights of channels are increased in the same manner as 
the weights of beams, Fig. 29, and the comments regarding beams 
in this respect apply to them. 

Characteristics and. Uses. Channels, like beams, are much 
stronger in one direction than in the other. This makes them suit- 









STEEL CONSTRUCTION 


29 


able for use as beams when the loads are applied in the plane of the 
web. However, they are not so economical as I-beams and require 
more lateral support to keep them from buckling. 

Hence, they are not used for this • purpose except 
when there is some condition which makes them 
specially suitable. This occurs around wellholes in 
floors, against walls, where nailing strips are to be 
bolted on, in wall spandrels or lintels, etc. 

The most important use of channels is in the 
construction of columns and truss members. For 
this purpose they are used in pairs connected to¬ 
gether with lacing, tie plates, or cover plates. They 
are also used to some extent for girder flanges and 
for many miscellaneous purposes. , 

Angles. Standard and Special Sections. There 
are two styles of angles: angles with equal legs and angles with 
unequal legs, Fig. 30. An angle is designated by the lengths of the 
legs and the thickness or the weight per lineal foot, thus: 




Fig. 29. Show¬ 
ing Method of 
Increasing Sec¬ 
tion of Chan¬ 
nels 


L 4" X 4" X f" 
or L 4" X 4" X 15.7#, 


L 6" X 3|" X |" 
or L6"X3|"X11.7# 

The standard sizes of angles with equal legs are 2, 2\, 3, 3^, 
4, 6, and 8 inches, respectively. There are a number of special sizes, 
the most important of which is 5 inches. The l§-inch angle is 
seldom used in structural work. 

The standard sizes of 
angles with unequal legs 
are 2 Y X 2", 3" X 2 Y, 3|" 

X2§", SY X 3", 4" X 3", 

5" X 3", 5" X 3 Y, 6" X 3Y> 

6" X 4". The important 

. .. . . Fig. 30. Details of Angle Sections 

special sizes usually obtain¬ 
able are 3" X 2", 7" X 3 Y, 8" X 6". 

Each size of angle is furnished in several thicknesses varying 
by xV inch. Although some of the smaller sizes of angles are made 


















STEEL CONSTRUCTION 



in less thickness than | inch, this is the minimum that should be 
used for structural purposes. On important work the minimum 
should be § inch. The minimum and maximum thickness, for the 
several sizes are given in the handbook and need not be repeated here. 

Angles are increased from the minimum thickness by spreading 
the rolls. In Fig. 31 the minimum thickness is shaded and the 
added metal unshaded. As the thickness is increased, a correspond¬ 
ing amount is added to the length of each leg. In 
the case of larger sizes, some mills use two sets of 
rolls, as has been described for I-beams. This 
p, additional length of the legs of angles must be 

^^/£ /?///// ^ B‘ t a ^ en into account in allowing for clearance. The 


1 


Fig. 3i. showing actual length of legs for any angle is easily com¬ 
puted, thus: L 3" X 3" X f"; minimum thickness 
for this size increase over minimum §", length 


Method of Increas¬ 
ing Section of An¬ 
gles 


of leg 3" + 


3 // 

8 


— Q3W 

— Os . 


Problem 

Compute the actual lengths of legs for the maximum thickness of all the 
standard and special angles listed in the handbook. Assume a second set of rolls 
is used on the following sizes: 5"X4"Xins"; 4"X4"X5 ff ; 3£"X3£"XU; 


>2 

5"X3Uxr; 5"X3 ff xT; 4 r X3i'xr; 4 ff X3"xr; 


6" X 4" X A 
8"X8"Xf" 


2 , 
9 //. 


5"X5"Xt 


9 


6"X6"XH"; 7'X3FXi 


3//. 

f 


8"X6"X| 


3 V. 


Record the results in the handbook in the tables of “Properties.” 

The results in the above problem may not agree with the sizes 
of angles furnished by the various mills but will be sufficiently exact 
for the uses of the designer. 

Characteristics and Uses. Angles are the most adaptable of the 
structural sections. They are used with 
plates or other shapes in built-up mem¬ 
bers, such as columns, plate girders, etc.; 
for connecting members together, as beams TH/CffK5s 
and girders to columns; as beams for 
special conditions of loading, as lintels; Flg - 32 - Detail s of Zee Bar 
singly or in pairs as struts; singly or in pairs as tension members. 

Zees. Standard Sections. A Zee, Fig. 32, is designated by its 
nominal depth and thickness, thus: 



Z3"xr 


The sizes listed by the Carnegie Steel Company are 3, 4, 5, and 6 













STEEL CONSTRUCTION 


31 


inches, respectively. The thicknesses vary by T V inch. The mini¬ 
mum and maximum thicknesses are: 

for 3" Z, \ n and T V 
/ for 4" Z, \ n and f 

for 5" Z, A" and \Y 
for 6" Z, and Y 

Zees are increased in thickness by spreading the rolls. In Fig. 33 
the shaded portion indicates the minimum section, and the unshaded 
part the additional section. The thickness of its 
web and flanges are increased equally, and thereby 
the depth of web and width of flange are increased 
by the same amount. Three sets of rolls are used 
for each depth, so that the overrun is tV inch for 
3-inch zees and J inch for larger sizes. 

Uses. Zee bars have been used extensively for columns, but 
they are rapidly becoming obsolete and should not be used unless 
there is some special reason for so doing. 

Tees. Standard Sections. A Tee, Fig. 34, is designated by the 
width of flange, length of stem, and weight per lineal foot, thus: 

T 4" X 3"X9.3# * T 3" X 4"X9.3# 

always giving the width of flange first. 

Some recent handbooks do not list tees. The sizes that have 
been available range from U X 1" X 1.0# to 5" X 3" X 13.6# with 
more than’50 intermediates. These are listed and their properties 
given in the Carnegie Steel Company’s “Pocket Companion”, 1913 
edition. 

Characteristics and Uses. As indicated above tees are going 
out of use, and as the demand decreases they will become more 


(V///SSSV 


Fig. 3.3 Showing 
Method of In¬ 
creasing Section 
of Zees 



Fig. 34. Typical Tee Sections 


difficult to obtain. The section is not an economical one for the 
common uses of structural steel. It is not efficient as a beam or 
as a strut, and is not suited for use in built-up sections. 


















32 


STEEL CONSTRUCTION 


It is well adapted for supporting book tile in ceiling and roof 
construction, Fig. 35. In cases where the T-section is needed to 




\\\\\ 






Fig. 35. Section Showing Tees Supporting Book Tile 


meet any special condition it can be made up of two angles placed 
back to back. In this manner a large variety of tees can be made. 

Plates. Standard Sizes. A Plate, Fig. 36, is designated by 
its width and thickness, thus: 

PI. 48" X T V 

or by its width and weight per square foot, thus:’ 

PI. 36" X 10.2# 

The former method is used on design drawings for structural steel 
work, and the latter on mill orders and shop details, also on design 
drawings for tank work. 

Plates are made in thicknesses varying by A inch from A inch 
up to 2 inches. Steel plates thinner than A inch are called “sheets” 
and are not used for structural work. The minimum thickness com¬ 
monly used is \ inch, and on many jobs nothing less than | inch is per¬ 
mitted. Plates thicker than 1 inch are seldom used on account of 



difficulty in punching. When a greater thickness is needed, it is 
made up of two or more plates. 

Styles. There are two styles of plates: the Universal Mill 
Plate, or Edged Plate, and the Sheared Plate. 




























STEEL CONSTRUCTION 


33 


The Universal Mill Plate is rolled to exact width, the width 
being controlled by a pair of vertical rolls as previously described 
and illustrated, Fig. 22. They vary in width by intervals of 1 inch 
from 6 inches to 48 inches. 

Sheared plates, as the name indicates, are sheared to required 
width after rolling. The stock sizes range in width from 24 inches 
to 132 inches in intervals of 6 inches, but they can be furnished in 
any intermediate width, even in fractions of an inch. 

The extreme lengths of plates that can be furnished are given 
in the handbooks. This data should be consulted to determine 



whether the required lengths can be obtained. In many cases the 
web plates of girders must be spliced on this account. 

Plates alone are not used for structural members. They are 
used in built-up members, such as columns and girders; for web and 
cover plates; and to connect members together. 

H-Sections. The H-section, Fig. 37, is designated by the name 
of the maker, the depth, and the weight per lineal foot, thus: 

Carnegie 8" H 34.0# 

Bethlehem 14" H 98.8# 

The H-section is not standard. At this time it is made only by the 
Carnegie Steel Company and the Bethlehem Steel Company. The 
Carnegie H’s* are 

8" H 34.0# 5" H 18.7# 

6" H 23.8# 4" H 13.6# 

There is but one weight for each size. 


♦Apply to the nearest office of the Carnegie Steel Company, or the Illinois Steel Company, 
for circular giving properties, or see Carnegie Steel Company s Pocket Companion, 1913 edition. 


























34 


STEEL CONSTRUCTION 


The nominal sizes of the Bethlehem H-sections are 8, 9, 10, 11, 
12, 13, and 14 inches, respectively. The actual sizes range from 
7 1 inches to 16| inches in intervals of g inch. The extreme weights 
are 34.6 pounds and 291.2 pounds per lineal foot. 

The H-sections are designed for use as columns and struts. 
They are not intended to be used in built-up members, except a 
special section which is designed to be increased by adding flange 
plates. 




Miscellaneous Sections. In addition to the regular structural 
sections just described there are a number of special sections, Fig. 
38, with which the designer should be familiar, viz: 

(a) Railroad Rails (e) Steel Sheet Piling 

(b) Wide-Flanged Channels (f) Steel Railroad Ties 

(c) Bulb Beams (g) Square Root Angles 

(d) Bulb Angles (h) Hand Rail Tees 

(i) Checkered Floor Plates 

These sections are not often used in steel construction for buildings, 
but occasionally conditions have to be met to which some of them 
are specially suited. 

































STEEL CONSTRUCTION 


35 


PROPERTIES OF SECTIONS 

Under the heading “Properties of Sections” the handbooks give 
tables of the numerical values of the various functions of the sec¬ 
tions. Referring to these tables, certain items need no explanation, 
viz: dimensions; thickness of metal; area; weight per lineal foot. 
Other items are not self-evident and will be explained in detail. 

Center of Gravity ( C.G .). See “Strength of Materials” for 
definition. The I-beam, H-section, and Z, Fig. 39, being symmetrical 


a a a 



a 


Fig. 39. Location of Center of Gravity of Sections. Values of x, x‘, and x* to be taken from 

Tables in Handbook 


about both axes, the center of gravity is in the center of the web 
and no values are given in the handbook tables. The C-section, 
Fig. 39, is symmetrical only about the axis which is perpendicular 
to the web; the center of gravity must, therefore, lie on this axis. 
The table gives the distance of the center of gravity from the back 
of the channel. 

Angles not being symmetrical about either axis, the center of 
gravity must be located by dimensions from the backs of both legs. 
If the legs are equal, both dimensions are the same; if the legs are 
unequal, the dimensions are unequal, the distance from the short 
leg x' being greater than that from the long leg x, Fig. 39. 










































36 


STEEL CONSTRUCTION 


The position of the center of gravity must be known in order 
to compute the moment of inertia of the section and the moments 
of inertia of built-up members. The former values are given in 
the tables; the latter must usually be computed by the designer. 

Illustrative Example. Compute the position of the center of 
gravity of L4" X 4" X disregarding fillets and rounded corners, 
Fig. 40. Divide the angle into two rectangles (1) and (2) as shown. 
Their centers of gravity are at c, and c 2 . 

Area of (1) 4 " X Y ■= 2.00 sq. in. 

Area of (2) 3|" X Y = 1.75 sq. in. 

Total area 3.75 sq. in. 

Moments about a! a' for (1) = 2.00 X ? = 0.50 
Moments about a' a ' for (2) = 1.75 X 2| = 3.94 

Total moment 4.44 

4 44 

Distance x = ~ 1*18' 


Similar computations apply about 
the axis b'b' and give the same result. 

Problem 

Compute the position of the center of 
gravity of the following: 

L5’X3'Xf' 

15" C 33# 

Moment of Inertia (7). Refer 
to “Strength of Materials” for defi¬ 
nition and method of computing 
moment of inertia. Moment of 
inertia is designated by the letter 
7. When a subscript is added 
it indicates which axis is used. Thus I a means the moment of 
inertia about the axis a. Note that this symbol is the same as is 
used for the beam. Care must be taken to avoid confusion. The 
meaning can be determined in each case by the context. The 
tables in the handbook give the value of 7 about both of the rec¬ 
tangular axes of the section and, in the case of angles, about a 
diagonal axis also. The position of this diagonal axis is so chosen 



Fig. 40. Diagram Showing Computation 
of Position of Center of Gravity 
of Angle 













STEEL CONSTRUCTION 


37 


as to give the minimum value of I. For I-beams and channels the 
minimum value is about the axis parallel to the web. 

The moment of inertia enters into the formulas for bending 
and for deflection. It is also used in computing the radius of gyra¬ 
tion of columns. Its values are given in the handbooks for the 
structural shapes and for plates, but it must 
be computed for most built-up sections, espe¬ 
cially for plate girders. The factors entering 
into the computation of the moments of inertia 
are always in inches. 

Illustrative Examples. 1. Compute I a 
and h for the plate shown in Fig. 41. 


1 


h =^X 8 X 1 X 1 X 1 = § 

X Lt 


h =fxX 1 X SX8 X 8 = 42§ 

s 



Fig. 41. Diagram for Moment 
of Inertia of Rectangular 
Plate 


2. Compute I a for the plate girder 
section in Fig. 42 made of 1 PI. 42" X ¥ and 
4Ls 6" X 6" X ¥- 

i 

for 1 PI. 42" X ¥ la (from tables) =3087 
for 4 Ls 6" X 6" X ¥ L (from tables) 

4 X 19.91 = 80 

for 4 Ls 6" X 6" X ¥ h 4 X 5.75 X 

19.57 X 19.57 = 8809 

,11.976 

Deductions for rivet holes at m 
Area of 2 holes = 2 X l¥ X ¥ = 

2.625 sq. in. 

For 1 hole Id — ts X 1^ X « W X ¥ 

X V = .08 

(a value so small that it is 
neglected) 

l a = 2.625 X 18.75 X 18.75 = 923 

Total net value I a = 11,053 



l 


Fig. 42. Diagram for Moment 
of Inertia of Plate Girder 




























38 


STEEL CONSTRUCTION 


Problems 

1. Compute the values of / for the section in Fig. 43. Deduct rivet 
holes. The section is made up of 4 Ls 6"X4"X re" connected with lacing bars 
(lacing not figured). 

2. Compute the values of I for the 
section shown in Fig. 44. 

1 C 12"X2(H# 



Fig, 43. 


1 L 4"X3"xr 

The axes a a and b b are through the 
center cf gravity The section not being 
symmetrical, the position of the center of 
gravity must be computed. 

Radius of Gyration (r). The 

radius of gyration is a value de¬ 
rived from the moment of inertia, but as its definition involves higher 
mathematical relations it need not be given here. It is reoresented 
by r, and is expressed in inches. 

The radius of gyration is derived from the moment of inertia 
by dividing by the area A in square inches and taking the square 
root of the result. This is expressed by the formulas 


Diagram for Moment of Inertia 
of Four Angles 


a 



Fig. 44. Diagram for 
Moment of Inertia of 
Channel and Angle 



Illustrative Examples. 1. Referring to Fig. 
41, the value of h = 42§; and A =8X1=8 
sq in. Therefore r 2 = 42§-i-8 = 5j, or r = V5J 
= 2.31". 

2. Referring to Fig. 42, the value of I a = 
11,976 (disregarding rivet holes). To find the 
radius of gyration 


fl PI. 42" X V =21 sq. in.l 
(4 Ls 6" X6" X ¥ = 23 sq. in-/ 


= 44 sq. in. 


r 2 


11,976 

44 


272.2 


r = V272.2 = *16.5" 


♦Refer to the textbook on Arithmetic for method of extracting the square root. Tables 
are given in the handbooks from which the values can be taken. 





























STEEL CONSTRUCTION 


39 


Problems 

1. Compute the values of r for the sections given in Figs. 43 and 44. 

2. Check the values given in the handbook for r fora 12" X 31 §#. 


The radius of gyration is used in the column formula as explained 
later in the text. 

. Section Modulus the f° rm ula for the resisting mo¬ 

ment of sections subjected to bending occurs the expression in 
which 7 is the moment of inertia and c is the distance from the 


neutral axis to the extreme fiber of the section. - has a definite 

c 

value for each section, and is called the section modulus. It saves 
one operation in arithmetic to have these values given for the various 
sections and they are given in the handbooks. As indicated by the 

fraction the value of the section modulus is determined by divid- 
c 

ing the moment of inertia by the value of c. 

Illustrative Examples. 1. Compute - for an 8" I 18# about 

c 

the axis perpendicular to the web. 

From the table, 7 = 56.9. The distance c is half the depth =4" 


7 

c 


56.9 


= 14.2 


2. Compute - for a channel 12"X20.5# about the axis par- 

' c i 

allel to the web. Not being a symmetrical section it has two values; 

From handbook, 7 = 3.91; c= (2.94 —.70) =2.24, and c = 0.70. 

. 7 

• • 

c 


—— = 1.75 and - = Ml = 5.59 
2.24 c 0.70 


Problem 

Compute the values of — for 

15" I 42# about axis parallel to web 
9" I 21# about axis perpendicular to web 
15" I 33# about axis perpendicular to web 
L 3"X3"Xf" about axis at 45° to legs 
L 6"X4" X h" about axis parallel to short leg 


Miscellaneous Properties. The handbooks include in the 
tables values of other properties of sections such as Coefficient of 
Strength, Coefficient of Deflection, and Resisting Moment. 





40 


STEEL CONSTRUCTION 


Strictly speaking, these are not properties of the sections, as they 
depend upon the value of the unit stress. They will be discussed 
in the text relating to beams. 

GENERAL INFORMATION 

Price Basis. The designer needs to be posted on the basis of 
prices for structural steel. For a number of years Pittsburgh, 
which has been the recognized center of steel production, has been 
the basing point for steel prices. Given a certain price for steel at 
Pittsburgh, the price at any other point is determined by adding 
to the base price the freight from Pittsburgh. Thus, if the price 
of steel at Pittsburgh is $1.50 per hundred pounds, the price in Chi¬ 
cago is $1.68 per hundred pounds, the freight rate being (at the time 
of writing) 18 cents per hundred pounds. 

Certain sizes of material are called “base” sizes. They are 
usually sold at a uniform price. The base sizes are: I-beams, 3 
inches to 15 inches, inclusive; angles, 3 inches to 6 inches inclusive; 
channels, 3 inches to 15 inches inclusive; tees, 3 inches and over; 
zees, all sizes. I-beams over 15 inches, angles over 6 inches, and 
angles and tees under 3 inches are charged for at a higher rate, 
usually 10 cents per hundred pounds, above base price. Special 
ections and sections rolled exclusively by one manufacturer are 
sold at prices varying from the base price according to market 
conditions. The base price itself varies from time to time, usually 
from $1.25 per hundred pounds to $1.50 per hundred pounds; occa¬ 
sionally it goes beyond these limits. 

Mill and Stock Orders. Structural steel orders are handled 
on two bases: (a) based on securing the plain material for the job 
from the rolling mills; (b) based on securing it from stock. Of 
course there may be a combination of the two. 

The mill basis is cheaper, as it eliminates waste, saves expense 
of handling, saves interest cost on the value of material, and may 
save a profit or premium demanded by the dealer for quick service. 
Consequently all work is carried out on the mill basis, if the time 
allowed for completion permits it to be done. 

When the material is to be furnished on the mill basis, the 
engineer who makes the detail drawings or the engineering depart¬ 
ment of the fabricating company makes a list of the individual 


STEEL CONSTRUCTION 


41 


pieces required. These pieces are then ordered from the rolling 
mills, cut to the lengths required (a small variation in length is 
usually allowed; short pieces are usually ordered in multiple lengths). 
Thus there is practically no waste of material. 

Material carried in stock is ordered from the rolling mills in 
lengths as long as can be handled conveniently. The lighter sec¬ 
tions are ordered in lengths of 30 feet and 36 feet, and the heavier 
sections in lengths of 60 feet. In cutting this stock material there 
is necessarily considerable waste. This stock material is not usually 
available direct from the rolling mills. The dealers in stock are 
usually fabricating companies, jobbers, or brokers. They charge 
an advance in price over the mill price to cover waste, handling, 
cutting, and other expenses incidental to the business, and to cover 
such profit as the market condition may permit. This advance 
in price varies from 10 cents to 50 cents per hundred pounds. 

Stocks of plain material are carried in all the larger cities. 
Printed lists of the material on hand are issued at frequent intervals. 
These lists should be consulted and used as a guide in selecting the 
sections that are to be used in all cases where stock is required. 

Whether mill or stock material will be used depends upon the 
size of the job and the time service required. Small jobs, say less 
than 100 tons, will usually be taken from stock unless only one or 
two sections are required. If delivery of fabricated material is 
required within 60 days, it will usually have to be taken from stock. 
Even for much more extended deliveries, all or part of the material 
must be taken from stock,* if there is a great demand. 

Variation in Weight. Attention is called to the provision in 
the specifications, p. 360, which permits a slight variation in the 
w T eight of the finished steel as compared with its theofetical weight. 
This variation in the case of sections other than plates is 2.5 per cent 
above or below the theoretical weight. This represents the prac¬ 
ticable limits in adjusting the rolls of the mill. The variation 
applies to individual pieces and not to a bill of steel as a 
whole; some pieces will be overweight and some underweight, 
so that the average on a bill of considerable size should agree 
very closely with the theoretical weight. In the case of plates, 


♦Apply to the nearest dealer for a copy of his stock list. Use it in solving the problems in 



42 


STEEL CONSTRUCTION 


a much larger variation is allowed, amounting in some cases to as 
much as IS per cent. It will be noticed that this variation is greater 
when plates are ordered to be of a certain gage or thickness than 
it is when they are ordered to be of a certain weight. The reason 
for this is that plates are slightly thicker in the middle than they 
are along the edges and, therefore, as the thickness must necessarily 
be measured near the edge, there is an excess of metal near the 
middle of the plate which is not counted. This excess is due to the 
springing of the rolls. Plates can be ordered by weight, that is, 
to have a certain weight per square foot of surface, and when so 
ordered the allowable variation is less because the rolls can be 
adjusted to give the average weight. The result is that the fabri¬ 
cating shop usually orders large plates by weight per square foot. 
In a job involving a large amount of plate work, as for chimneys, 
tanks, etc., this may become a matter of importance, but for build¬ 
ing work a relatively small number of plates are required and it is 
not customary to specify them by weight, but by thickness. 

QUALITY OF MATERIAL 

Reliability of Structural Steel. Structural steel is the most 
reliable material used in building construction. Its manufacture 
has been a continuous development to the extent that the quality 
of material produced is under almost absolute control. The ingredi¬ 
ents are tested and measured before being put into the furnace, and 
the product is analyzed and tested physically to make sure* that it 
fulfills the required standards; so that, with a reasonable amount of 
inspection and test, the purchaser can have definite assurance that 
he is securing the quality of material which he needs. 

The manufacturers and users of structural steel have co-oper¬ 
ated in developing the material in order to attain the most prac¬ 
ticable results. On the one hand, the manufacturers have insisted 
on keeping the quality such as to m&ke its manufacture commercially 
satisfactory. On the other hand, the users of steel have demanded 
the best material that it is possible to make and still keep within 
reasonable limitation of cost of manufacture. 

STANDARD SPECIFICATIONS 

As a result of the efforts of the manufacturers and users, 
Standard Specifications h^ve been formulated covering the quality 


STEEL CONSTRUCTION 


43 


of structural steel. There are three sets of specifications that may 
safely be used, viz:* 

(a) Manufacturers’ Standard Specifications for Structural 
Steel—Class Bt 

(b) Standard Specifications for Structural Steel for Build¬ 
ings, adopted by the American Society for Testing 
Materials (Given in full p. 359) 

(c) Specifications for Structural Steel, adopted by the 
American Railway Engineering Association 

Comparison of Specifications. A brief comparison of the pro¬ 
visions of these three sets of specifications is of interest. 

Range of Application. The specifications (a) and (b) are 
intended primarily to apply to steel for building work, whereas (c) 
is for railway bridges. In buildings, the greater part of the load to 
be supported is permanent or dead load. The variable or live load 
usually is applied gradually, without shock or vibration. In railway 
bridges the conditions are quite different. The permanent load for 
a short span is the smaller part of its capacity. The live load, being 
much larger than the dead load and being applied quickly, produces 
great shocks and vibration. Because of these conditions, specifica¬ 
tion (c) is more rigorous in its requirements than are (a) and (b). 

Process of Manufacture. Specification (c) requires the open- 
hearth process of manufacture; (a) and (b) permit either open- 
hearth or Bessemer. 

Chemical Analysis. Specification (c) requires the chemical 
analysis to report the percentages of sulphur, phosphorus, carbon, 
and manganese, and limits the amount of Sulphur; (a) and (b) limit 
the phosphorus. 

Tensile Strength. Specification (c) places the desired ultimate 
tensile strength of steel sections at 60,000 pounds per square inch, 
allowing a variation of 4000 pounds, thus making the range of 
strength 56,000 to 64,000 pounds; (b) allows a range from 55,000 
to 65,000 pounds; (a) allows the same range as (b) and in addition 

* (a) Published in the handbooks issued by the Steel Manufacturers; (bt Published by 
American Society for Testing Materials, Edgar Marburg, Secretary, University of Pennsylvania, 
Philadelphia, Pa.; published in full in Carnegie Steel Company’s Pocket Companion, 1913 
edition; -(c) Published by American Railway Engineering Association, 910 South Michigan Boule¬ 
vard, Chicago, III. 

t Class A is for railroad bridges. 



44 


STEEL CONSTRUCTION 


permits a maximum of 70,000 pounds if the percentage of elongation 
is the same as for steel having a tensile strength of 65,000 pounds.. 

Rivet Steel Strength. Specification (c) specifies the desired 
strength of rivet steel at 50,000 pounds, allowing 4000 pounds vari¬ 
ation, thus making the range of strength from 46,000 to 54,000 
pounds; (a) allows a range from 46,000 to 56,000 pounds; and (b) 
allows a range from 48,000 to 58,000 pounds. 

Elongation and Fracture. The three specifications are in close 
agreement as to their requirements for elongation of the test speci¬ 
men and the character of fracture. 

Bending Requirements. Specification (c) is somewhat more 
rigorous than the others in the bending requirements. 

Either of these specifications will give satisfactory results, but 
specification (b) of the American Society for Testing Materials is 
recommended as being most suitable for building work. It is given 
in full on p. 359. 

DISCUSSION OF IMPORTANT FEATURES 

Method of Manufacture. A brief description has been given 
of the two methods of manufacture of steel. The Bessemer process 
is more rapid and, as a result, is less subject to accurate control than 
the open hearth. In the Bessemer process the operator is governed 
by the character and color of the flame issuing from the converter. 
He must learn by experience to do this, as the whole matter depends 
upon his judgment. The open-hearth process, being slower, gives 
an opportunity to take samples and make analyses, and thus control 
* the operation. 

The Bessemer process, as ordinarily conducted, does not remove 
sulphur and phosphorus, so that whatever quantities of these unde¬ 
sirable elements are in the iron ore remain in the finished steel. On 
the other hand, the usual open-hearth practice reduces the amount 
of sulphur and phosphorus, these elements being removed in the slag. 

For the above reasons, the product of the open-hearth furnace 
is considered more desirable than that of the Bessemer, when steel 
is to be subjected to severe use, as in the case of railway bridges. 

Heretofore the question has been an economic one. The Bes¬ 
semer process being the cheaper, most of the producing capacity 
was of that type, and a higher price was charged for open-hearth 


STEEL CONSTRUCTION 


45 


steel. Recently the situation has changed. Most of the new 
furnaces are open-hearth and no extra charge is demanded for steel 
made by this process. There is now no difficulty in securing it. 

Chemical Composition. Carbon. The essential elements of 
steel are iron and carbon. All of the other elements found may be 
considered as impurities. The iron, of course, constitutes all but a 
small percentage of the total. The function of the carbon is to 
make the steel hard and strong. Within certain limits the tensile 
strength of steel increases, while the ductility decreases, with the 
increase in the amount of carbon used. The amount of carbon in 
structural steel varies from 0.10 per cent to 0.40 per cent. The 
smaller amount occurs in rivet steel. For structural shapes, the 
usual limits are 0.15 per cent to 0.25 per cent. A larger amount 
makes steel too hard for structural purposes. 

Steel to be forged or welded needs to be low in carbon. Steel to 
be tempered must be high in carbon. These features do not con¬ 
cern structural steel. 

Phosphorus. Phosphorus occurs as an impurity in the iron ore. 
It is not practicable or necessary to remove all of it. It increases 
the strength of the steel but produces brittleness. The amount of 
phosphorus allowed is about 0.10 per cent. 

Sulphur. Sulphur is also found as an impurity in the iron 
ore. Its presence in the steel causes trouble in rolling. It usually 
amounts to less than 0.05 per cent. 

Silicon. Silicon may be in the pig iron or may be absorbed 
from the material used in lining the steel furnace. It increases 
the hardness of the steel and has a beneficial effect in the process of 
manufacture, so that the presence of a limited quantity, about 0.20 
per cent, is not objectionable. 

Manganese. Manganese also may be found in the iron ore, 
but if not, it is added during the process of manufacture to assist 
in the chemical transformations. Its presence in the finished steel 
to the extent of about 1.0 per cent is an advantage, as it adds to the 
strength and improves the forging qualities. However, some 
authorities believe that it promotes corrosion of steel and on this 
account is objectionable. 

Alloys of Steel. A much larger quantity of manganese is 
sometimes used as an alloy, but such a steel is not used for structural 


46 


STEEL CONSTRUCTION 


purposes. There are many alloys of steel, developed for special 
purposes. The only one used for structural work is nickel steel, and 
up to the present time its use has been limited to a few large bridges. 
Probably nickel steel will not be economical for building work for 
some time. 

Physical Properties. The determination of the physical prop¬ 
erties most suitable for structural steel has been a gradual develop¬ 
ment. It has been influenced by the cost of manufacture and ease 
of fabrication on the one hand, and uniformity and economy to the 
consumer on the other. 

The manufacturers have required that such limits be set as would 
permit them to operate economically. Expensive refinements of 
small importance have been eliminated. The allowable range in 
strength has been made large enough so that it can easily be attained. 
The fabricating shops have encouraged the use of a material that 
can easily be punched and sheared. 

The designing engineers representing the consumers have de¬ 
manded a small range in strength and uniformity in physical proper¬ 
ties, and at the same time as great strength as is consistent with relia¬ 
bility of material, with economy of manufacture, and with ease of 
fabrication. 

As the physical properties are closely related to the uses of the 
steel, their requirements are much more explicit than are those 
relating to chemical composition. The chemical tests are of inter¬ 
est only to the extent that they indicate physical properties. Thus, 
high carbon and high phosphorus indicate high tensile strength and 
brittleness, but these properties can be determined more directly by 
the tension test, with the attendant observations of elongation and 
character of fracture. 

Railway Bridge Grade Steel. It has been noted that the Manu¬ 
facturers’ Standard Specifications (a) provide for steel, which has 
a maximum strength five thousand pounds greater than the strength 
provided by specifications (b) and (c). This grade of steel was 
formerly very much used for building work, but now steel having the 
lower strength is generally used. The reason for using the lower 
strength steel is that it is more reliable and more uniform in quality. 
The higher the strength the more brittle the material, hence the 
greater danger of injury from careless handling and from the shop 


STEEL CONSTRUCTION 


47 


operations of fabricating. This latter-condition makes the fabricating 
shops prefer to use the softer grade. It seems probable that this 
harder grade of steel will be used less and less and, therefore, more 
difficult to get; so it is wise to specify the railway bridge grade, which 
is Class A, in case Manufacturers’ Standard Specifications are used. 

Yield Point. The yield point indicates one of the most import¬ 
ant properties of structural steel. When a piece of steel is subjected 
to a tensile stress, it elongates, the amount of the elongation within 
certain limits being proportional to the load applied;.thus, if a piece of 
steel of one square inch cross section is subjected to a load of 5000 
pounds, and then to a load of 10,000 pounds, the elongation in the 
second case will be twice as much as that in the first case. The test 
for the strength of the steel specimen, as described in the specifica¬ 
tions, is made in a tension or pulling machine, to which is attached 
a lever arm carrying a weight, corresponding to the beam of an 
ordinary scale. If the load is increased at a uniform rate, the 
weight on the scale beam, by being moved at a certain uniform 
rate, will keep the beam exactly balanced until about one-half the 
ultimate strength of the material is reached; then the scale beam 
will drop, which indicates that the specimen has begun to elongate 
at a more rapid rate. The stress in the steel at which this occurs 
is called the “yield point” of the steel. 

Breaking Load. If the load which produced the above effect were 
applied continuously for a long time, the specimen would finally 
break; but usually in testing, additional load is applied at the 
same rate as before until the specimen breaks. The breaking load, 
according to the specifications, should be about 60,000 pounds per 
square inch. This represents the load which will break the steel if 
applied within a relatively brief period of time, but a much smaller 
load will break it if applied over a long period of time. 

Elastic Limit. The change in the rate of elongation does not 
occur just at the point where it becomes manifest by the action of 
the scale beam, but at a somewhat lower stress. The point where 
the change actually occurs is called the “elastic limit”. This term 
formerly was used in specifications and, in fact, still is used in the 
Manufacturers’ Standard Specifications, but as the commercial 
methods of testing structural steel do not clearly show the exact 
point of the elastic limit, the yield point is u§ed. 


48 


STEEL CONSTRUCTION 


Yield Point and Factor of Safety. The Standard Specifications 
require that the yield point shall be not less than one-half the ulti¬ 
mate strength. The value of the yield point is usually several 
thousand pounds above this amount. When the yield point is 
reached, the material has begun to fail. This value, therefore, in¬ 
stead of that for the ultimate strength, is the one which should be 
used in computing the factor of safety. If the yield point is at 32,000 
pounds and the unit stress 16,000 pounds, the factor of safety is 2 
instead of 4, as commonly stated. Refer to the discussion of 
factor of safety, p. 7. 

Reduction of Area. The provision in the specifications re¬ 
garding the reduction of area of the' test piece at the point 
of fracture is of importance, as it indicates thg ductility of the metal. 
If the piece breaks without much reduction in area, it indicates that 
the material is hard and probably brittle. Such material is likely 

to break, if subjected to shock, and may 
fracture in punching and shearing The 
character of the fracture is indicative of the 
same condition. If cup-shaped and silky in 
appearance, it indicates toughness; but if the 
fracture is irregular, it indicates brittleness. 
The bending test also is important for deter¬ 
mining whether the steel is tough or brittle. 

Inspection and Tests. In order to check the quality of the 
steel as it is made, tests are made of each melt. The chemical 
analysis is made from a sample taken from the molten metal as it 
comes from the furnace or converter. Sometimes a check analysis 
is made from drillings taken from the rolled sections. 

Physical tests are made in accordance with the requirements of 
the standard specifications. The test specimens are cut from the 
finished structural steel. The bend test is made by bending the 
specimen around a pin whose diameter equals the thickness of the 
specimen, Fig. 45. Rivet rods must bend flat on themselves. These 
tests are made with cold steel. The work is done either by blows 
or by pressure. To pass the test, the specimens must show no 
fracture on the outside of the bent portion. 

The tension-test specimen is shaped as shown in Fig. 46. It is 
put in a tension-testing machine and pulled until it breaks. From 



a ~) 

f 



L 

y 

_1* 

( O S 

V_ ) 

rOR 

STRL/C TURAL 

S TCCL 

( 



\ 

\ _ 



i 


rOR Ril'd T 5 TdCL 

Fig. 45. Bending Tests for 
Steel 









STEEL CONSTRUCTION 


49 


this are determined the total strength, yield point, elongation, and 
character of fracture, Fig. 47. 

Records of these tests are furnished to customers if desired. 


I TO 3 RAL. 

--~<L_ 


PARALLEL SECT/ On 


HOT LESS THAN 3' 


n? 


ABOUT 3 


ETC. 


ABOUT /8 


ABOUT E 

i 


PIECE TO BE OF SAME THICKNESS AS THE PLATE. 

Fig. 46. Tension Test Piece 


Customers may, and on important jobs do, employ inspectors to 
supervise the tests. These inspectors also make a surface inspection 
to see that the finished sections are straight and free from cracks, 
blisters, buckles, and slivers. Fig. 48 is a specimen report of tests. 




Fig. 47. Test Piece Before and After Being Broken by Tension 


UNIT STRESSES 

\ 

General Discussion. The unit stress, or working stress, is the 
stress or load that is allowed on each square inch of cross section of 
the metal and is expressed jn pounds per square inch. There is 























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Fjjt. 48. Sample Report of Inspection Tests 




































STEEL CONSTRUCTION 


51 


practical agreement on the values used for the various kinds of 
stress. The following values can be used with assurance that they 
will give safe results. Note that these values are for building work; 
they may also be used for highway bridges but not for railroad 
bridges. 

Structural Steel. Structural steel is so dependable and of such 
uniform quality that the values for unit stress are well established. 
The values given follow standard practice. 

Maximum Allowable Stresses on Structural Steel in Pounds per 


Square Inch: 

Axial tension net section. 16,000 

Bending on extreme fiber, tension. 16,000 

Bending, on extreme fiber, compression. 16,000 

Bending on extreme fiber, of pins. 25,000 

Shear on shop-driven rivets. 12,000 

Shear on field-driven rivets and turned bolts. 10,000 

Shear on rolled-steel shapes. 12,000 

Shear on plate-girder webs. 10,000 

Bearing on shop-driven rivets and pins. 25,000 

Bearing on field-driven rivets and turned bolts. 20,000 

Axial compression on columns. 16,000 — 70-^- 


In the above, / is the length of the column in inches from center to 
center of bearing, and r is the least radius of gyration. The maxi¬ 
mum value allowed is 14,000 pounds per square inch. 

For wind pressure alone or combined with gravity loads, the 
unit stresses may be 50 per cent in excess of those given above, but 
the section must not be less than required for the gravity loads alone. 

The discussion under “Columns” should be consulted regarding 
limitations of the use of the compression formula and the conditions 
under which higher and lower values are used. 

Cast Iron. There is not such close agreement among engineers 
as to the unit stresses allowable on cast iron. The following values 
represent fairly well the current practice; they are in pounds per 
square inch. 


Axial tension. n °t allowed 

Bending on extreme fiber, tension. 3,000 

Bending on extreme fiber, compression. 10,000 

Shear. 2,000 

Compression. 10,000—00 — 


















52 


STEEL CONSTRUCTION 


The discussion of cast-iron columns should be consulted for 
limitations of values used and length of columns. These values are 
taken from the Building Ordinances of the City of Chicago. 

Masonry. As the ultimate bearing of steel work is on masonry, 
and as the bearing values are necessary in designing the bearing 
plates and column bases, the values are given for the usual forms of 
masonry. The values below, expressed in pounds per square inch, 


are taken from the Building Ordinances of the City of Chicago. 

Coursed rubble, Portland cement mortar. 200 

Ordinary rubble, Portland cement mortar. 100 

Coursed rubble, lime mortar. 120 

Ordinary rubble, lime mortar. 60 

First-class granite masonry, Portland cement mortar.600 

First-class lime and sandstone masonry, Portland cement 

mortar. 400 

Portland cement concrete, 1-2-4 mixture, machine mixed. 400 

Portland cement concrete, 1-2-4 mixture, hand mixed. 350 

f ... 

Portland cement concrete, l-2*/j-5 mixture, machine mixed. . . 350 

Portland cement concrete, 1-2]/£-5 mixture, hand mixed.300 

Portland cement concrete, 1-3-6 mixture, machine mixed. 300 

Portland cement concrete, 1-3-6 mixture, hand mixed.250 

Natural cement concrete, 1-2-5 mixture. 150 

Paving brick, mortar 1 part Portland cement, 3 parts torpedo 

sand.;. 350 

Pressed brick and sewer brick, mortar same as above.250 

Hard common select brick, same as above. 200 

Hard common select brick, mortar, 1 part Portland cement, 

1 part lime, 3 parts sand. 175 

Common brick, all grades, Portland cement mortar. 175 

Common brick, all grades, good lime and cement mortar . . . 125 

Common brick, all grades, natural cement mortar. 150 

Common brick, all grades, good lime mortar. 100 


The American Railway Engineering Association permits a 
bearing of 800 pounds per square inch on concrete, provided the 
area of the pier is twice the area of the base plate. The writer 
would allow this high stress only when the concrete is properly 
reinforced with hooping, similar to that used in hooped columns. 


RIVETS AND BOLTS 

Ordinary Sizes. The sizes of rivets vary in a general way with 
the thickness of steel which they connect. In structural steel work 
the sizes commonly used are | inch, l inch, and £ inch, the f-inch 




















STEEL CONSTRUCTION 


53 


size being used much more than any other. In very light work 
^-inch rivets are sometimes used and, in very heavy work, rivets 1 
inch, lg inches, and 1| inches are used. 

Rivets smaller than £ inch are used when the size of the mem¬ 
bers connected requires it, or when the thickness of metal used is 
chiefly £ inch, f-inch rivets must be used in the flanges of 6-inch 
and 7-inch I-beams; 6-inch and 7-inch channels; and 2-inch angles, 
f-inch rivets can be used in all of the beams, channels, and angles 
larger than the above sizes. |-inch rivets may be used in beams 
18 inches and larger, and angles 3 inches and larger. 

Another consideration that sometimes affects the sizes of rivets 
used, and concerns particularly the sizes larger than f inch, is the 
thickness of metal to be joined together. It is the general experi¬ 
ence in shops that satisfactory punching cannot be done when the 
thickness of metal is greater than the diameter of the hole to be 
punched. Of course, it is possible to punch thicker material than 
this, but it is troublesome to do so because of the frequent breakage 
of punches. Consequently if most of the material to be punched is 
l inch in thickness, |-inch rivets will be used. 

Another approximate rule governing the size of rivets is that in 
general the diameter of the rivet shall be not less than one-fourth of 
the total thickness of metal. 

The use of more than one size of rivet on a job is to be avoided 
as much as practicable on account of the trouble and expense of 
frequently changing the punches. It is especially inconvenient to 
punch more than one size of hole or drive more than one size of rivet 
in a structural member. 

Spacing. There are a number of conditions that control the 
spacing of rivets. These have been developed into practical rules 
which are quite uniform among the various fabricating shops. 
Rivets spaced too close together would cut out too large a percentage 
of the cross section of members. Rivets spaced too far apart cause 
a waste of material in connecting pieces. 

The specifications relating to rivet spacing,* p. 365, items 57 
to 63, are in accord with usual practice and should be followed. 


♦From "Specifications for Structural Work of Buildings” by C. C. Schneider, M. Am. Soc. 
C. E., published in Transactions of the American Society of Civil Engineers, Vol. LIV (June, 1905), 


p. 498. 



54 


STEEL CONSTRUCTION 


TABLE I 


Gages for Angles 


j. 



Leg 

8" 

7" 

6" 

5" 

4" 

3F 

3" 

L 


■-N 

G, 

G* 

G 3 

Max. Rivet 

3" 

3" 

1 i* 

1 8 

4" 

2\" 

3" 

1" 

3F 

2\" 

2 ¥ 

7 V 

8 

3" 

2" 

1 3* 

1 4 

7 v 

8 

2Y 

7// 

8 

2" 

7 V 

8 

13 V 

1 4 

7// 

8 


- ^ , 

Cj , 





Leg 

2Y 

2" 

13 n 

1 4 

1 i" 

1 2 

13V 

1 8 

H" 

1" 

3 V 

4 

G t 

g 2 

1 3 V 

1 8 

1 I" 

1 8 

1" 

7 n 

8 

7 V 

8 

3 n 

4 

51/ 

8 

1 v 

2 

• • • 

• • . 

• • • 

• . • 

• • • 

• • • 

• • • 

• • • 

G, 

• • • 

• • « 

• • • 

• • • 

• • • 

• • • 

... 


Max. Rivet 

3 V 

4 

5 » 

8 

Iff 

2 

3 V 

8 

3 V 

8 

3 V 

8 

1 tf 

4 

IV 

4 


Gage. The term “gage” is used to designate the spacing of 
rivet lines parallel to the axis of the member. For example, 
Fig. 49 illustrates the gage lines of beams, channels, and angles. 
Standard values are assigned in the hand-books to the gage lines in 
the flanges of I-beams and channels, and in angles. However, as 
manufacturers do not agree as to the gage lines of angles, values 
used by the American Bridge Company are given, Table I. 

Gage lines in webs of beams and channels and in plates are not 
standard and are located according to requirements. 



Pitch. By the pitch of rivets is meant the spacing along the 
gage lines, Fig. 49. Some of the rules for this spacing are given in 
Schneider’s Specifications previously referred to. Note carefully 



























































STEEL CONSTRUCTION 


55 


the provisions there given. The rule usually followed for the mini¬ 
mum pitch is three times the diameter of the rivet. But this mini¬ 
mum should be used only when necessary, it being preferable to use 
a larger spacing of rivets under ordinary conditions. Three inches 
is desirable for f-inch rivets, where this spacing does not involve 
the use of an excess of material in the connected pieces. Where no 
definite stress occurs in the rivet, as in built-up columns, or where 
the stress is small, as in certain portions of flanges of plate girders, 
six inches has been established as the maximum. In case there are 
two gage lines closer together than the minimum spacing allowed, the 
rivets in the adjacent rows must alternate so that the diagonal dis¬ 
tance between them will exceed the minimum by 40 per cent or 
more. 

Edge Distance. If holes are punched too close to the edge of 
the metal, the tendency is to bulge out the metal and perhaps to 
crack the edge. This necessitates maintaining a certain distance 
from the edge to the center of the rivet holes. This distance must 
be greater in the case of a sheared edge, as of a plate, than is required 
for a rolled edge, as the flange of a beam, an angle, or a universal 
mill plate. The values commonly used are given in Schneider’s 
Specifications quoted above. 

In the smaller sizes of beams and channels, the gage distances 
do not comply with these specifications. The width of flange is 
not sufficient to permit the use of the full edge distance and still 
allow necessary clearance from web to permit driving. On account 
of the danger that the metal will bulge out or crack along the edge, 
designers should try to avoid using smaller than 10-inch I-beams and 
channels in a way that will require flange punching. Instead, 
web connections or clips and clamps can generally be used. 

Clearance. A hole cannot be punched close against the web of 
an I-beam or close to the leg of an angle. A certain amount of 
space is required for the die. Of course holes can be drilled in any 
position, but this is not resorted to unless there is some particular 
reason for so doing. However, tire punching of holes is not the 
limiting feature in the matter of rivet clearance. The required 
clearance is governed by the size of the die used in forming the rivet 
head. The usual rule for clearance is one-half the diameter of the 
rivet head plus three-eighths of an inch. The clearances required for 


56 


STEEL CONSTRUCTION 


various conditions for several sizes of rivets are given in Fig. 50, 
which represents the practice of the American Bridge Company. 

Closely associated with the 




C 




MIN. 

£ 

,r 

ff 

V 


z:x 


STD. 

if 

/V 

*r 

'i 


IZL 




37- 


3 


w 

FOR 


RIVETS 


amount of clearance is the ac¬ 
cessibility for driving the rivets, 
Fig. 51. For power driving, the 
rivet must be so situated that it 
can be brought between the jaws 
of the riveting machine. For 
riveting with the percussion ham¬ 
mer (air hammer), it must be 
possible to hold on to one head 
of the rivet with a die while the 
other head is formed by the riv¬ 
eter. For hand riveting it is 
necessary to be able to hold on to one head of the rivet and 
that the other end of it- be accessible for driving with a maul. 
It is sometimes necessary to cut away flanges of I-beams or cut 
holes in the webs of box girders to make the rivets accessible for 
driving, Fig. 51. This matter is generally looked after in making 
shop drawings, but needs some attention in designing. 


V 

V 

f" 

*8 


Fig. 50. Clearance Allowed for Riveting 




USUAL METHOD IMPOSSIBLE TO 

OF Off/V/HO DRIVE BY 

USUAL METHODS 










- 1 


CUTAWAY TO 
PERMIT DRIVING 


BE DRIVEN AFTER 
BEAMS ARE 
ASSEMBLED 


Fig. 51. Difficult Situations for Riveting 


Rivet Heads. Manufacture. Rivets are made with one head. 
This is done by heating a length of rivet rod to the proper tempera¬ 
ture and running it into the rivet machine. The machine upsets 
the end of the rod, making a head, and then cuts off the rivet to the 
desired length. It is necessary that the dies in which the heads 
are formed be of proper size and be kept in perfect condition in order 
to make good rivets. If the two halves of the die which grip the 
sides of the rivet do not fit closely, some of the metal will be forced 































STEEL CONSTRUCTION 


57 



PRCi/rrrrs PROPER DRIVIN6 

Fig. 52. Defective Rivets 


between them, forming fins on the sides of the rivets, Fig. 52. If 
the corners of the die become rounded, a shoulder will be formed at 
the junction of the shank with 
the head. Either of these de¬ 
fects will prevent the rivet head 
from fitting up tight against the 
plate, thus causing unsatisfac¬ 
tory results when driven. This 
point is especially important in 
tank work where the rivets must be water-tight. 

Button Head. The shapes of the rivet heads vary among 
different makers, although these variations are slight. The type 
of head used in structural work is called the “button head” to dis¬ 
tinguish it from the cone head which is used in tank and boiler work. 

Flattened and Countersunk Heads. It is sometimes necessary 
to flatten rivet heads for special situations in order to provide the 
required clearance for an adjacent member. This flattening may 
vary from a slight reduction from the full thickness of the head 
down to a flush or countersunk head. The different thicknesses 
ordinarily used are f inch, j inch and | inch. A countersunk rivet 
is one in which the head is made in the form of a truncated cone and 
is formed by driving in a hole which has been tapered by reaming 


FORMULAS 

a-dX/5+& a-D/AM. OF HEAD 

t> ■ a X 4ZS t> -HE/GH T 

e -b x/ S e.-L ONO RADIUS 

C-t> C -SHORT RADIUS 



Diana. 

Diana. 

FULL DRIVEN HEAD 

COUNTERSUNK 

of 

of 













Rivets 

Holes 

Diam. 

Height 

Radius 

Radius 

Diam. 

Depth 

d 


a 

b 

C 

e 

g 

h 

K 

iV 

H 



76 

n 

A 

K 

& 

Vs 

K 

Vs 


n 

K 

K 

H 


H 

n 

H 

i 

A 

% 

H 

IK 

U 

u 

H 

i A 

K 

Vs 

H 

1A 


H 

59 

64 

IK 

A 

l 


IK 

n 

H 

1 TJ 

i A 

A 

lK 

__ 

1H 

<» 

_ &A _ 

49 

6 4 

_ 

IK 

— A _ 


Fig. 53. Proportions of Rivets in Inches 
From American Bridge Company 










































58 


STEEL CONSTRUCTION 


so that the diameter at the outside is greater than at the inside of 
the plate. The sizes of rivet heads are shown in Fig. 53. The 
conventional signs for riveting are given in the handbooks. 

It is to be noted that countersunk rivets are not as strong as 
rivets with button heads and are much more expensive, conse¬ 
quently they are not used unless absolutely required by the condi- 



Fig. 54. 100-Ton Hydraulic Riveter, 120-inch Gap 

Courtesy Mackintosh, Hemphill <fc Company 

tions. A flattened rivet should be used in preference to a counter¬ 
sunk rivet; but when a smooth surface is to be obtained, the head 
must be countersunk and chipped flush with the pla,te. 

Driving. Before rivets can be driven, the pieces to be joined 
must be assembled accurately in position and be held together with 
bolts. The number of bolts used for this purpose will depend to 
















STEEL CONSTRUCTION 


59 


some extent on tlie accuracy of the punching and the straightness of 
the pieces. If the several pieces are not held together, the metal of 
the rivet will be forced out between them, or the driving of adjacent 



Fig. 55. Hanna Pneumatic Kiveter, 24-inch Gap 
Courtesy Vulcan Engineering Sales Company 


rivets may draw the plates closer together and loosen the rivets 
previously driven. 

Rivet holes are punched & inch larger than the nominal size 
of the rivet for when the rivet is heated, it expands somewhat, 
making it necessary to have the larger size hole. The driving of 
the rivet must be done in such a way as to upset the metal of the 
shank so that it fills the rivet hole solidly, even to the extent of 
filling out any irregularities in the hole, and then the button head 



60 


STEEL CONSTRUCTION 


must be formed on the driving side. As the rivet cools, it shrinks 
and thus grips the steel more tightly than when first driven. 



Fig. 56. Rivet Ready for Driving 
Courtesy Vulcan Engineering Sales Company 


Riveting Machines in Shop. In the shop, rivets are driven with 
an hydraulic riveter, Fig. 54, or a pneumatic riveter, Fig. 55. The 



Fig. 67. Three Stages in Process of Riveting 


machine consists essentially of a yoke which spans the members 
to be riveted, Fig. 56. On the outer arm of the yoke is a die which 










































STEEL CONSTRUCTION 


61 




fits over the head of the rivet; the other arm carries a similar die, 
or rivet set, which pushes against the end of the rivet, upsetting the 
shank of the rivet and thus forming a head, Fig. 57 The power is 
applied by means of hydraulic or pneumatic pressure. The pressure 


Fig. 58. Pneumatic Riveting Hammer 
Courtesy Chicago Pneumatic Tool Company 

is held on until the rivet is partly cooled and has acquired enough 
strength so that the spring of the plates will not stretch it. 

Pneumatic Hammer. Whenever the rivet is in such position 
that it cannot be reached by means of the power riveter, it is driven 


Fig. 59. Light Motor-Driven Punch 
Courtesy Mackintosh, Hemphill & Company 

with a pneumatic hammer. The rivet is inserted in the hole and 
held in place by means of a die pressed against the head, the die 
being held in position by hand or by a suitable arrangement of 
levers. The pneumatic riveter, or air gun. Fig. 58, carries a die. 




62 


STEEL CONSTRUCTION 


or set, for upsetting the rivet and forming the head. When the ' 
power is turned on, this machine delivers very rapid blows and thus 
performs the required work. Riveting in the field on the assembled 
structure is usually done by means of the pneumatic hammer. 

Hand Riveting. Hand riveting is now used only on small jobs, 
the air gun being replaced by the sledge hammer. The rivet is 
first hammered down by blows from the sledges, then the- rivet 
set is applied and sledged to form the head to its proper shape. 

Perfect rivets can be driven by either of the above methods. 



Fig. 60. Heavy Motor-Driven Multiple Punch 
Courtesy of Mackintosh, Hemphill & Company 


Punching and Reaming. Rivet holes in structural steel work 
are ordinarily punched in the metal by means of a powerful punching 
machine, Figs. 59 and 60 showing examples of the single and multi¬ 
ple types, respectively. The essential features of the machine for 
doing this work are a punch and a die. The die is usually about 
& inch larger in diameter than the punch. The two are placed 




STEEL CONSTRUCTION 


63 


in the machine so that their axes are exactly in line. The 
plate is placed over the die and the punch is forced through, thus 
shearing out a round piece. This resulting hole is not perfectly 
smooth. The degree of roughness will depend on the condition of 
the punch and die, and the amount of difference in their diam¬ 
eters. The metal around the hole is to some extent torn and 
distorted. 

For ordinary structural purposes the holes are accurate enough 
and the damage to the metal so slight that no further treatment is 
needed, but in railroad structures and sometimes for special cases 
of building work it is required that the holes be reamed. In such 
cases the hole is punched smaller than the size of the rivet—called 
“sub-punching”—and it is then enlarged to the proper size by 
means of a drill or reamer. In railroad bridge construction, it is 
custoipary to ream all metal over f inch in thickness and to ream 
all holes for field connections. In structural work for buildings, 
reaming is not required to such a great extent. Sometimes it is 
required on metal thicker than £ inch and on field connections of 
very heavy members where a slight inaccuracy would occasion 
serious inconvenience in erecting. 

Where the several pieces assembled together have a thickness 
of more than four times the diameter of the rivet, or where through 
any inaccuracy of punching the holes do not match accurately, the 
holes should be reamed to true them up; but in such cases they need 
not be sub-punched and the. reaming only serves the purpose of 
trimming up the irregularities. 

As previously stated, the diameter of the rivet hole as punched 
is I’g inch larger than the diameter of the rivet; but in order to take 
account of the injured metal in computing the net section, the hole 
is figured § inch larger than the rivet. 

Functions of Rivets and Bolts. Rivets and bolts are used for 
fastening together the several sections used in building up the 
structural steel members and for connecting the members together 
in the finished structure. Rivets are always used for this purpose 
unless there is some special reason for using bolts. Generally 
speaking, rivets are cheaper than bolts and for most purposes more 
effective. They fill the holes full even though the holes may be 
slightly irregular in shape, and if driven tight will remain so; whereas 


64 


STEEL CONSTRUCTION 


bolts, unless they are turned and driven tight into reamed holes, 
are apt to become loose after a time. 

The function of rivets is to hold one piece of steel to another 
and to transmit stress from one to the other. In so doing they 
must resist a bearing pressure and a shearing stress. 

In many cases the rivets are not subjected to any definite shear¬ 
ing or bearing stress, but simply serve to hold the steel sections 
together in built-up members. They are unquestionably subjected 
to some stresses, but it is not possible to determine just what these 
are. In such situations the spacing of rivets is governed by rules 
resulting from practical experience. 

It sometimes happens that the direction of the stress applied 
to the rivet is along its axis, that is, the rivet is subjected to tension. 
It was formerly the custom to specify that rivets should not be 


4000 






zr~ 


f 


V7 


30 


4000 


7 



4000 , $? n f 

hn 

r 

m - 

-— -r^r- | 


1 p 



i 

fj 

4000 7j» 1 7 

7 

Mi 


lJ 


(b) 


Fig. 61. Diagrams Showing Stresses in Rivets 


subjected to tension, but that bolts should be used in such situations. 
This provision was necessary when wrought-iron rivets were in use, 
as their heads could be easily broken off. Steel rivets are much 
more reliable in this respect and, if properly driven, can be sub¬ 
jected to tension as safely as bolts. 

Bearing. Fig. 61-a represents two pieces, m and n, riveted 
together, so that the stress (4000 pounds) in m is transmitted to n. 
Fig. 61-b represents three pieces riveted together so that the stress 
(8000 pounds) in the center piece m is transmitted to the two out¬ 
side pieces l and n. 

The bearing on the rivet is the pressure exerted on it by the 
plate through which it passes. In Fig. 61-a the bearing from plate 
m is on the right half of the rivet and from plate n on the left half 
of the rivet. Although the actual bearing is on the curved surface, 




























STEEL CONSTRUCTION 


65 


i. e., one-half the circumference of the rivet, the area used in figuring 
is the projected area of this surface, i. e., the thickness of the plate 
multiplied by the diameter of the rivet. For the plate m, the area 
is § w Xf" or .375 sq. in., and for plate n, §"Xf" or .281 sq. in. 

The unit stress allowed in bearing is 25,000 pounds per square 
inch for shop-driven rivets; thus the allowed values in bearing are 
for m 0.375 X 25,000 = 9375 # 
for n 0.281X25,000 = 7025# 

The stress actually transmitted is 4000 pounds, and each bearing must 
be good for at least this amount, hence the bearings are sufficient. 

The actual bearings per square inch are 

for m 4000-b 0.375 = 10,600# 
for n 4000-7-0.281 = 14,200# 

Problem 

Compute from the above data the allowable bearing values for m and n and 
the actual bearing per square inch on m and n for field-driven rivets. 


In Fig. 61-b the stress is transmitted from the plate m to the 
plates l and n and divided equally between them. The bearing 
areas are 

form ¥ X f" =0.375 sq. in. 

for l and n combined 2 Xf"Xf" = 0.5625 sq. in. 

The allowed bearing values on shop-driven rivets are 

form 0.375 X25,000= 9375# 

for l and n combined 0.5625X25,000 = 14,065# 

The stress actually transmitted is 8000 pounds, so that the bearing 
for m is 8000 pounds and for l and n 4000 pounds each; hence, the 
bearings are sufficient. \ 

The actual bearings per square inch are 

form 8000-7-0.375 =21,300# 

for l and n combined 8000-7-0.5625 = 14,200# 

Problem 

Compute from the above data the allowable bearings for l, m, and n for 
field-driven rivets. 


Shear. Referring again to Fig. 61-a, the forces acting on the 
two plates tend to cut, or shear, the rivet along the plane between 
the plates. This shearing action is resisted by the cross-section 

7T^2 * % • • 

area of the rivets. This sectional area is —, which in this case is 


68 


STEEL CONSTRUCTION 


In a perfect design these three elements would be equal in value, 
but this ideal is rarely reached. Most frequently it is the shearing 
value which determines the strength of the joint, next the bearing 
value, and least frequently the section of the metal. 

Illustrative Example. Fig. 62 illustrates a splice of two plates, 
each 7"Xf". Rivets f" diameter, field driven. 

(a) Using all of the ten rivets, 

Shear value 10 X4418 = 44,180# 

Bearing value 10 X5625 =56,250# 

Tension value at (1) ' 65 X|X 16,000 = 36,750# 

Tension value at (2) 5| Xf X 16,000 = 31,500# 

Loss of tension value between (1) and ( 2 ) = 5,250# 

As this loss is more than the amount transmitted from m to n by the 


r 



—< 

• - 

-1 

> - 

- < 

1 — 


i 

\ 


—< 

1 — 

- < 

1- 

-1 

1 — 

1 1 f 

1 1 

1 

/ 

z 

j 

a , 

X 

6 

7 


Fig. 62. Diagrammatic Views of a Riveted Joint 

rivet at (1), the entire tension value at (1) is not available and the 
strength of the joint is the tension value at (2) plus the shear value 
of the rivet at (1), or 31,500+4418 = 35,918#. 

(b) Now consider that the rivets at (1) and (7) are omitted. 

Shear value 8X4418 =35,344# 

Bearing value 8x5625 =45,000 # 

Tension value at (2) 5|X|X16,000 = 31,500# 

The strength of the joint is the tension value at (2), i. e., 31,500#. 

(c) Next consider that the rivets (4) are omitted. 

Shear value 8 X4418 = 35,344# 

Tension value at (2) plus shear value of rivet at (1) as 

above = 35,918# 




















STEEL CONSTRUCTION 


69 


The strength of the joint is the shear value 35,344$. 

(d) Finally omit the rivet at (3). 

Shear value 9X4418 = 39,762$ 

Strength of joint same as in (a) =35,918$ 

From the above it is clear that the maximum strength of the joint 



R! GH T WRONG 



RIGHT WRONG 



RIGHT WRONG 

Fig. 63. Diagrams Showing Right and Wrong Arrangement of Rivet 
Holes in Tension Members 


that can be made in this case is 35,918 pounds. It requires 9 rivets 
as in (d). Nearly the same strength can be secured with 8 rivets as 
in (c), 35,344 pounds. 





H" 

Rivet 

Vs " 

Rivet 


w 

Rivet 

yy 

Rivet 

a 

b 

b 

a 

b 

b 

1 

1 Ys 


5 

3r? 

3ts 


1 Vs 

2 

5V 2 

3H 

3V 2 

2 

2jt 

2Y 

6 

3 % 

3 5 A 

2^ 

2V 4 

2& 

6^ 

3V 2 

3H 

3 

2i« 

2 Ys 

7 

3Vs 

3Vs 

3V 2 

2& 

0 13 
*^16 

7'A 

3 % 

4 

4 

013 

^16 

3 

8 

3Vs 

4H 

4K 

0 15 
^16 

3^ 

sy 2 

4 

4 H 


a=Sum of gages minus thickness of angle 

Yz Rivets can be taken at ]/%" less than for 
Rivets 

1" Rivets can be taken at }/%" more than for 
Yz" Rivets 


Note 


Fig. 64. Stagger of Rivets Required to Maintain Net Section. 
From “Standards for Detailing ” American Bridge Company 









































































70 


STEEL CONSTRUCTION 


The important point to be observed from this example is the 
difference between (a) and (b); the loss of section by rivet holes 
should be made as gradual as possible. 

Problem 

Go through the operations of the above example on the basis of shop rivets. 

Net Section. The holes in angles can usually be arranged so 

that only one need be deducted 
with two or three rows, and two 
with four rows. This is not 
always true for the large angles. 
Fig. G3 illustrates the right and 
wrong arrangement of holes in a 
number of. cases. Fig. 64 illus¬ 
trates the pitch of staggered 
rivets required to maintain the 
net section. If the joint is in 
compression no deduction is made in the cross section on account 
of rivets, and the rivets need not be staggered unless required for 
minimum spacing. 





\ 63000* 

Fig. 66. Side and End View of a Riveted Hanger 


Problems 

1. Fig. 65 shows two angles in tension to be connected to a gusset plate 
with shop rivets. Determine the following: 

Size of rivets 
Net section of angles 




































STEEL CONSTRUCTION 


71 


Tension value of net section 

Thickness of gusset plate to develop the full double shearing value 
of the rivets 

Number of rivets 

Locate gage line and space the rivets 
Draw plan, elevation, and section of joint at f-inch scale 
Note. The connection illustrated is poor on account of secondary stress, 
p. 234. It is used only for practice. 

2. Fig. 66 shows a hanger connected to the underside of an I-beam. 
The hanger is made of 2 Ls 4"X3"X|" and carries a load of 65,000 
pounds. Determine the following! 

Size of rivets 

Total section of two angles 

Net section of two angles after deducting one rivet hole from each 
Whether section is sufficient for the load applied 
Thickness of gusset plate to develop the double shearing value of rivets 
Number of shop rivets to connect lug angles to main angles (assume 




Side and End View of Standard Beam Connection 


that one-half of load is transmitted through the lug angles) 

Number of shop rivets to connect hanger to gusset plate 
Number of shop rivets to connect gusset plate to top angles 
Number of field rivets (in tension) to connect top angles to I-beam 
Make drawing at i-inch scale, showing all dimensions and rivet spacing 

Give page numbers of handbook for all references used in the above opera¬ 
tions 

3 Fig. 67 shows the standard end connection for a 15" I 42#. What 
is the strength of the connection? 

Bolts.* The foregoing discussion of rivets applies also to bolts, 
except as to stresses allowed and as to bolts in tension. 

Turned bolts fitting tight in reamed holes have the same values 
as field rivets. Machine bolts should be allowed only three-fourths 
the unit stresses of field rivets, i. e., 7500 pounds per square inch 
shear and 15,000 pounds per square inch bearing. 

♦The student should obtain a catalogue from a bolt manufacturer and become familiar 
with the standard and special bolts on the market. 



























70 


STEEL CONSTRUCTION 


The important point to be observed from this example is the 
difference between (a) and (b); the loss of section by rivet holes 
should be made as gradual as possible. 

Problem 

Go through the operations of the above example on the basis of shop rivets. 

Net Section. The holes in angles can usually be arranged so 

that only one need be deducted 
with two or three rows, and two 
with four rows. This is not 
always true for the large angles. 
Fig. 63 illustrates the right and 
wrong arrangement of holes in a 
number of. cases. Fig. 64 illus¬ 
trates the pitch of staggered 
rivets required to maintain the 
net section. If the joint is in 
compression no deduction is made in the cross section on account 
of rivets, and the rivets need not be staggered unless required for 
minimum spacing. 





Fig. '66. Side and End View of a Riveted Hanger 


Problems 

1. Fig. 65 shows two angles in tension to be connected to a gusset plate 
with shop rivets. Determine the following: 

Size of rivets 
Net section of angles 





































STEEL CONSTRUCTION 


71 


Tension value of net section 

Thickness of gusset plate to develop the full double shearing value 
of the rivets 

Number of rivets 

Locate gage line and space the rivets 

Draw plan, elevation, and section of joint at f-inch scale 

Note. The connection illustrated is poor on account of secondary stress, 
p. 234. It is used only for practice. 

2. Fig. 66 shows a hanger connected to the underside of an I-beam. 
The hanger is made of 2 Ls 4"X3"X|" and carries a load of 65,000 
pounds. Determine the following! 

Size of rivets 

Total section of two angles 

Net section of two angles after deducting one rivet hole from each 
Whether section is sufficient for the load applied 
Thickness of gusset plate to develop the double shearing value of rivets 
Number of shop rivets to connect lug angles to main angles (assume 




Fig 67 Side and End View of Standard Beam Connection 

that one-half of load is transmitted through the lug angles) 

Number of shop rivets to connect hanger to gusset plate 
Number of shop rivets to connect gusset plate to top angles 
Number of field rivets (in tension) to connect top angles to I-beam 
Make drawing at j-inch scale, showing all dimensions and rivet spacing 

Give page numbers of handbook for all references used La the above opera¬ 
tions 

3 Fig. 67 shows the standard end connection for a 15" I 42#. What 
is the strength of the connection? 

Bolts.* The foregoing discussion of rivets applies also to bolts, 
except as to stresses allowed and as to bolts in tension. 

Turned bolts fitting tight in reamed holes have the same values 
as field rivets. Machine bolts should be allowed only three-fourths 
the unit stresses of field rivets, i. e., 7500 pounds per square inch 
shear and 15,000 pounds per square inch bearing. 

♦The student should obtain a catalogue from a bolt manufacturer and become familiar 
with the standard and special bolts on the market. 



























72 STEEL CONSTRUCTION 

In general, the use of bolts in the permanent structure should 
be discouraged, being limited to locations where it is impracticable 
to drive rivets and to connections where they serve simply to hold 
the members in position and do not transmit stress. The cost of 
using turned bolts will prevent their use where rivets can be used. 
But machine bolts are cheaper than rivets for most field connections 
and their use must be forbidden except in cases where they are 
suitable. 

Turned Bolts. Turned bolts, as the name indicates, are turned 
to exact diameter in a lathe. The holes Tor turned bolts must be 
reamed after the members are assembled, or both members must 

be' reamed to fit the same tem¬ 
plate. The reamer must have 
the same diameter as the finished 
bolt so as to give a driving fit. 

Washers must be used under 
both the head and nut. Refer 
to Fig. 68 and note that there is 
a fillet under the head. If the 
washer is not Used, this fillet will 
prevent the head from bearing 
against the plate. Tf the thread 
is cut long enough to allow the 
nut to bear against the plate, the 
thread will extend into the hole; 
hence a washer is used so that 
the thread need not be cut so long. After the nut is drawn up 
tight, the threads should be checked with a chisel so that it cannot 
become loosened. 

Machine Bolts. Machine bolts are made from rods as they 
come from the rolling mill and are not finished to exact size. They 
do not fill the holes fully. Their principal use is for assembling 
material in the shop or in the structure, preparatory to riveting. 
They may remain in the finished structure if not subjected to shear. 
Such a case is a beam resting on another. 

Bolts in Tension. When a bolt is used in tension, the net area 
available to resist the stress is the area at the root of the thread. 
For example, determine the tensile strength of a f-inch bolt. Re- 























STEEL CONSTRUCTION 


73 


ferring to the handbook, it is found that the diameter at the root of 
the thread is 0.62 inches. From this, the area, if not given in the 
table, can be computed and is found to be 0.30 square inch. Then 
the tension value is 0.30X10,000 or 3000 pounds. 

Two nuts should be used on bolts in tension to prevent strip¬ 
ping the threads, and the threads should be checked after the nuts 
are tightened. 

Length of Rivets and Bolts. The grip of a rivet or bolt is the 
thickness of the material through which it passes. The grip esti¬ 
mated is the nominal thickness of metal plus A inch for each piece 
of metal. 

The length of rivet required for a given case is the grip plus the 
amount of stock required to form the head and for filling the hole 
when the rivet is upset. The lengths required for various grips are 
given in the handbooks. 

The length of bolt required for a given case is the grip plus the 
thickness of the washers, plus the thickness of the nut (or two nuts 
if in tension), plus \ inch. 



CRANE COMPANY OFFICE BUILDING, .CHICAGO 
Holabird, & Roche , Architects 





















STEEL CONSTRUCTION 

PART II 


BEAMS 

Definitions. A beam is a structural member subjected to a load 
applied perpendicular to its longitudinal axis. Usually the beam is 
in a horizontal position and the load is applied vertically downward. 
It is supported at the ends (unless it is a cantilever). The space 
between the supports is the span. 

i_ 

The word beam is a general term which applies in all cases to 
a member subjected to bending by a transverse load, irrespective of 
the use to which it is put. There are a number of special terms 
which have reference to the position or use of the beam. 

A joist is a beam which supports the floor or other load direct. 

A girder is a beam which supports one or more joists or other 
beams. 

A lintel is a beam which supports the wall above an opening 

therein. 

A spandrel beam is one which supports the masonry spandrel 
between the piers of a wall. 

Elevator beams, sheave beams, stair stringers, crane girders, 
etc., are used for the purposes indicated by their names. 

Built-up beams are usually called “girders” irrespective of their 
uses. There are plate girders, box girders, beam box girders, etc. 

The span of a beam is the distance between supports, or, in the 
case of a cantilever, the distance from the support to the end of the 
beam. 

Classification. Beams are classified as simple and restrained. 
A simple beam is one which has a single span and merely rests on its 
supports, there being no rigid connection to prevent normal bending. 
A restrained beam is one which has more than one span or is rigidly 
connected at one or more supports, or otherwise prevented from 
normal bending. Fig. 69 illustrates a simple beam and several 




76 


STEEL CONSTRUCTION 


forms of restrained beams, showing in an exaggerated way the forms 
they assume u r hen bending under load. 

Although most beams in steel construction are somewhat 
restrained by their end connections, they are treated as simple 
beams in designing. Beams extending over more than two supports 
are very rarely used in building construction and are not considered 
in this text. Cantilever beams occur in the form of a beam pro¬ 
jecting from a support to which it is rigidly attached, and in the 
form of a beam spanning from one support to another, and pro¬ 
jecting beyond one or both supports. 

Sections. The structural steel section most used as a beam is 
the I-beam. It is designed for this purpose and is the most efficient 
form in which the steel can be made for resisting bending. Chan¬ 
nels, angles, and tees are used only to meet some special condition. 
The built-up or riveted girders imitate the I-beam and are used for 



Fig. 69. Simple, Cantilever, and Restrained Beams 


loads which are too great to be supported by the rolled section. 
This part of the text deals only with rolled sections. Riveted sec¬ 
tions are given later, 

REVIEW OF THEORY OF BEAM DESIGN 

Factors Required in a Complete Design. The complete design 
of a beam requires the computation of the bending moments and 
shears resulting from the assumed loading, and of the resisting 
moment, shearing resistance, and deflection of the beam section 
which it is proposed to use. The resisting moment usually governs. 

Maximum Bending Moment. The resisting moment based on 
the allowable unit stress must be equal to or greater than the maxi¬ 
mum bending moment. As the section of the rolled beam is the 
same from end to end, its resistance is constant throughout its 















STEEL CONSTRUCTION 


77 


length. Hence, it is necessary to compute only the maximum 
bending moment. The position and amount of the maximum 
bending moment are computed later in the text for various conditions 
of loading. 

Maximum Shear. The shearing resistance based on the allow¬ 
able unit stress must be equal to or greater than the maximum 
shear. The shearing resistance of the rolled beam is constant 
throughout its length. Hence, it is necessary to compute only the 
maximum shear. The position of maximum shear in single span 
beams is always adjacent to the support which has the greater 
reaction. 

Deflection. A beam subjected to bending stresses must have 
some deflection, and, under certain conditions, the amount of this 
deflection must be limited. For example, the floor section, Fig. 70, 
shows that the deflections in the joists were so great as to cause a 
bad crack m the marble floor above the steel girder. 


MARBLE RLOOR 




.OORy _ 

r v.r — 


• ' * * *, . *> *> " * •c ; ^ - v \h'.V *v* e 



CONCRETE EILL 

JOIST 

• 

GIRDER 


Fig. 70. Floor Section,Showing Crack Over Girder, Due to Deflection of Joists 


The definitions and methods of computing bending moments, 
shears, resisting moments, shearing resistance, and deflection are 
given in “Strength of Materials.” The student should review 
those topics before proceeding with this text. The following brief 
discussion may help to fix in mind the important points. 

Flexure. It is a matter of common observation that a loaded 
beam deflects or sags between the supports. This is most evident in 
wood beams, but is true of beams of all materials. This deflection 
stretches the fibers at the bottom of the beam, i. e., produces tension; 
and shortens the fibers at the top of the beam, i. e., produces com¬ 
pression. Somewhere between the top and the bottom the fibers 
are neither stretched nor shortened, hence there is no stress; this 
place is called the “neutral axis” and passes through the center of 
gravity. In I-beams and channels the neutral axis is at mid-depth. 













78 


STEEL CONSTRUCTION 


This is also true of rectangular wood beams. The intensity of 
stress—tension or compression—corresponds to the amount of defor¬ 
mation—lengthening or shortening; hence, the intensity varies with 
distance from the neutral axis, being zero at the neutral axis and 
maximum at the extreme fibers* at the top and bottom. This is 
illustrated in Fig. 71. The stress on the extreme fiber—not the 
average stress—governs in designing. The working or unit stress 
allowed is 16,000 pounds per square'inch in both the tension and the 
compression flanges. (See Unit Stresses, p. 51.) 

In Fig. 71 assume that each arrow represents the stress on a unit 
area, the length of the arrow representing amount or intensity of the 
stress. To find the resistance of the beam to bending it must be 
remembered that the resisting moment is the sum of the moipents 

of all stresses about the neutral 
axis. Under Strength of Beams, 
in “Strength of Materials,” Part 
I, it is shown that the resisting mo¬ 
ment is expressed by the formula 


— 

NEUTRAL AXIS ~2 

\ A 



TENSION 

\ X —- 

X=q 

1 _ x -i 


Fig. 71. 


Graphical Representation of Stresses in 
the Fibers of a Beam 


M-il 

c 


in which M is resisting moment in inch-pounds; / is the moment of 
inertia in terms of inches; c is the distance from the neutral axis to 
the extreme fiber in inches; and S is the maximum fiber stress, that 
is, the stress on the extreme fiber in pounds per square inch. From 
this formula the resisting moment of the beam can be computed. 

Assume a 12" I 31|$. From the handbook the value of I is 
215.8. Ihe distance from the neutral axis to the extreme fiber is 
6 inches. The allowable unit stress on the extreme fiber is 16,000 
pounds per square inch. Then. 



16,000X215.8 

6 


= 575,467 in.-lb. 


When the unit stress S, resulting from a given bending moment, 
is required, the formula is transposed into the form 



*The term extreme fiber is correctly used in relation to wooden beams as wood is a fibrous 
material. Steel is not a fibrous material but the term expresses the idea clearly and is generally 
used. 




















STEEL CONSTRUCTION 


79 


Assume that the bending moment is 500,000 inch-pounds and that 
the beam is 12" I 31^#, then, 


S = 


500,000X6 

215.8 


13,900# 


Vertical Shear. Fig. 72 illustrates a beam with a heavy load 
applied close to one support. There is a tendency for the part on 
the left of the vertical plane a a to slide downward in relation to the 
part on the right. This is prevented by the shearing resistance of 
the beam. This shearing tendency exists throughout the 0 length 
of the beam but is greatest near the supports. In this case the 
maximum shear is adjacent to the right support at a a and is 
assumed to be 45,000 pounds. It is resisted by the strength of the 
steel at this section. The average stress over this section is the 
total vertical shear divided by the area and is expressed by the formula 


in which S a equals shearing ~ _ ~ ' ~ „ 

Fig. 72. Diagram Illustrating Shear on a Beam 

stress per square inch; V equals 

total vertical shear; and A equals area in square inches. 
But it can be shown that the shear is not uniform over this area, 
being zero at the extreme fiber and a maximum at the neutral axis. 
The exact maximum value is difficult to compute, but it can be 
determined approximately by assuming that the entire shear is 
resisted by the web of the beam (see Resisting Shear, “Strength of 
Materials” Part II); then the above formula is used, making A equal 
the area of the web in square inches. In this case assume that the 
beam is 12" I 311#. The area of the web is approximately 12"X 

45 000 

.35" = 4.2 sq. in. Then S a = - ’ - or 10,714 pounds per square 

inch. The allowable value given under Unit Stresses is 10,000 
pounds per square inch, and the beam is over-stressed in shear. 

If it is desired to compute the maximum resistance to shear for 
this beam, the formula is put in the form 

U = S 8 X/1 

and for this case 

V= 10,000X4.2 = 42,000# 

A beam subjected to an excessive load would not fail by the 





80 


STEEL CONSTRUCTION 


actual shearing of the metal along the plane a a but by the buckling 
of the web. This has been taken into account in establishing, the 
unit stress. 

Deflection. As previously stated, a beam which is subjected 
to bending stresses must deflect a certain amount. The amount of 
deflection depends on the load, the length of span, and the section 
of the beam. It is expressed by the formulas: 

(1) For a uniformly distributed load 

5 W l 3 
384 El 


(2) For a load concentrated at center of span 

1 W * 
d- 48 El 


in which d equals deflection in inches; W equals total load in pounds; 
l equals span in inches; I equals moment of inertia; and E equals 
modulus of elasticity equals 30,000,000. 

Modulus of Elasticity. The modulus of elasticity is the ratio of 
the unit stress to the unit deformation. If a piece of steel one inch 
•square and ten inches long is subjected to a tensile stress of 20,000 
pounds, the unit stress is 20,000 pounds per square inch. The steel 


is elongated about 


1 

150 


inch and, therefore, the unit deformation, or 


the elongation of one inch in length, is —-— 
6 6 1500 

unit stress to unit deformation is —y—- = 

1500 


inch. Then the ratio of 
= 30,000,000. This ratio 


has been determined by experiment. It is the same for both tension 
and compression. Other materials have other values. 


CALCULATION OF LOAD EFFECTS 

Uniformly Distributed Loads. The first step in designing a 
beam is to determine the bending moments and shears resulting 
from the assumed loading. The methods of computing them are 
given under External Shear and Bending Moment, “Strength of 
Materials/’ Part I. 









STEEL CONSTRUCTION 


81 


Joists. The loads on joists are usually distributed uniformly 
along the length of the beam. Assume that the simple beam, Fig. 
73, has a span L=17'-6", and supports a load of 800 pounds per 
lineal foot. 


Total load = W — 17.5X800 
= 14,000# 

Since the load is uniformly distri¬ 
buted, the reactions are equal: 

/? 1 = /? 2 = i IF = li^ = 7000# 


ill 


iiiiiiiinii^iiiiiiriiiiniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiinT 

illllilllllllilllililllllllflllllHllllllllllllll!!llllllll 

I 





---- L-17-6"- - 

A 


ff t Pi 

Fig. 73. Diagram of Beam Uniformly Loaded 


The maximum shear occurs adjacent to each support and its 
amount is the same as the reaction, hence V t and V 2 have the same 
values as R t and R r 

The maximum bending moment occurs at the middle of the 
span and has a value 

m = r 2 x— 2 — Wx—~ 

/? 2 X^ = 7000X8.75 =61,250 ft.-lb. 

\Wx = 7000 X 4.375 = 30,625 ft.-lb. 

M = 30,625 ft.-lb. = 367,500 in.-lb. 

The formula for this bending moment is 

M = \ W L=lX 14,000X 17.5 = 30,625 ft.-lb. 


Cantilever Beam. Fig. 74 represents a cantilever beam support¬ 
ing a uniformly distributed load. Assume 
the length L of cantilever to be 8'-9", 
and the load, 800 pounds per lineal foot; 
then 

W = 8. 75X800 = 7000# 

R t = 7000# 

The maximum bending moment is at Fig. 74. Diagram of Cantilever 

0 Uniformly Loaded 

the support, and therefore 

M = WX^= 7000X4.375 = 30,625 ft.-lb. 

Compare these results with those obtained for the simple span 

























































82 


STEEL CONSTRUCTION 


having the same load per lineal foot. The span is one-half as much, 
while the shear and the bending moment are the same. 

Combination Simple and Cantilever Beam. A beam resting on 
two supports, projecting beyond one of them, and supporting a uni¬ 
formly distributed load is represented in Fig. 75. Assume the 
span L between supports to be 17'-6", the length L' of the canti¬ 
lever to be 8'-9", and the load 800 pounds per lineal foot; then 
W = (800 X17.5) + (800 X 8.75) = 21,000 # 

The reactions must be determined by the method of moments. 
Take the moments about /?,. For the positive moment the lever 
arm is the distance from /?, to the center of gravity of the entire 
beam, viz, 13.125 feet; therefore 

Positive moment = 21,000X13.125 = 275,625 ft.-lb. 



Fig. 75. An Overhanging Beam with Shear and Moment Diagrams 


The negative moment must equal the positive moment; then 

R 2 XL = 275,625 

and the value of R 2 is found by dividing the positive moment by the 
distance L between supports.' 



275,625 


15,750# 


Therefore 


17.5 














































































































































































































































































STEEL CONSTRUCTION 


83 


Now since the sum of the reactions must equal the total load, the 
value of R t can be determined by subtracting R 2 from W; then 

R t = 21,000 -15,750 = 5250 # 

This value of R t can-be checked by taking moments about I? 2 . 

The position of the maximum shear is not self-evident so the 
shear values must be computed. V t =5250. Proceeding toward the 
right, 800 pounds is deducted for each foot, so the shear becomes 
zero at 6.5625 feet from R t ; continuing to a point just to the left 
of R 2} the value of the shear is 

V 2 =5250 - (800 X 17.5) = -8750 # 

Continuing, to the right, add the value of R 2 ; then the value of the 
shear is 

V 3 = -8750+15,750 = +7000# 


Continuing, the shear reduces at the rate of 800 pounds per lineal 
foot, becoming zero at the end of the cantilever. The above values 
are shown graphically on the shear diagram. 

The maximum positive bending moment is between R t and R 2 
at the same position as the zero shear. Its value is 

f +5250X6.5625 « +34,448) 


i =+17,224 ft.-lb. 


.-800X6.5625X++.. -17,224, 


The maximum negative bending moment is at R 2 . Its value 
computed on the right is 

.8.75 


-800 X 8.75X- 

or computed on the left is 

'+5250X17.5 


-30,625 ft.-lb. 


= + 91,875" 


l- 800X17.5X 


17.5 


122,500 


1 = -30,625 ft.-lb. 


The moment diagram can be constructed by computing the values 
at points one foot apart and plotting the results. From this dia¬ 
gram it will be noted that the bending moment changes from positive 
to negative at the point x. This is called the “point of contra- 
flexure” and in this case it is located 13.125 feet from R t . 









84 


STEEL CONSTRUCTION 


It is usually easier to compute the bending moment for simple 
spans uniformly loaded from the formula 


M = 


W L 
8 


and for cantilevers from the formula 



For the combination span illustrated above, the maximum negative 
moment may be computed from the cantilever formula. But the 
maximum positive moment cannot be expressed in a simple formula 
and must be computed by means of the summation of moments as 
illustrated. 

EXAMPLES FOR PRACTICE 


1. A joist has a span of 21 feet. It supports a floor area 
>2 feet wide. The floor construction weighs 115 pounds per square 


T 

1 

'WFiirWIIB 

1 j.ll 1 

lire 

III 111 

T I’lT IV',, 'nn M !!' mu , I.'ir I'.'l |l|'|] I |l||:!| 

$oo" pcr uncAR /■rJliiijl | 1 |i|!l| 

1! 1 

illlii.'iMl 'Nil'll.'.!L i 


► 

•s. 

V’ 

-4-— 4-o — - 


Fig. 76. Uniformly Loaded Beam Overhanging at Both Ends. 


foot and the live load to be supported is 50 pounds per square foot. 
Compute the shear and bending moment. 

2. What are the maximum shear and bending moment for a 
total load of 80,000 pounds uniformly distributed on a span of 8 
feet; 10 feet; 12 feet; 14 feet; 16 feet? What is the ratio of the 
bending moments for the 8-foot, and the 16-foot spans? 

3. Compute the maximum shears and bending moments for a 
beam supporting a uniformly distributed load of 1,000 pounds per 
lineal foot on a span of 8 feet; 10 feet; 12 feet; 14 feet; 16 feet. What 
is the ratio of the bending moments for the 8-foot and 16-foot spans? 

4. Compute the maximum shears and bending moments for 
cantilevers from the data given for the preceding problem. Com¬ 
pare the results with those for the simple beam. 

5. Fig. 76 represents a beam extending beyond both supports. 
Its load is 600 pounds per lineal foot. What is the maximum 
shear? What are the bending moments at /?, and ft 2 ? What is 
the maximum positive bending moment? 




























STEEL CONSTRUCTION 


85 


6. Construct the shear and moment diagrams for the preced¬ 
ing problems. 

7. Given a span of 20 feet and a bending moment of 50,000 
foot-pounds, what is the total uniformly distributed load? 


50,000X8 

20 


20 , 000 # 


8. Given a span of 18 feet and a bending moment of 72,000 
foot-pounds, what is the load per lineal foot? 

Concentrated Loads. Girders in floor construction usually 
receive their loads at points 
where joists connect. 





. 3 

^4 

j— 3-0'^- 

— 4 l 0"— 

— 4'-0"—~ 

— 4-0 "-—» 

•2-0t J 




resents a simple beam supporting 
the concentrated loads P v P 2 , P 3 , 
and P 4 . The loads are 

P t = 60,000# 

P 2 = 80,000# 

P 3 = 80,000# 

P, = 50,000# Fig. 77. 

Total load =270,000# 

To determine the reaction P 2 , take moments about R l : 





Simple Beam with Concentrated Loads. 
Shear Diagram 


3X60,000 = 180,000 
7X80,000 = 560,000 
11X80,000 = 880,000 
15X50,000 = 750,000 


2,370,000 ft.-lb. 

7? z = 2 . 3 ^Q QQ = 139,412# 


Similarly, to determine the reaction R t , take moments about R 2 : 

2X50,000 = 100,000 
6X80,000 = 480,000 
10X80,000 = 800,000 
14X60,000 = 840,000 


2,220,000 ft.-lb. 

P, = 2 ’ 22 i ° 7 ,()0 - = 130,588 # 

Therefore 7^+7?, = 130,588+139,412 = 270,000# 

which checks with the total load. 























































































86 


STEEL CONSTRUCTION 


The maximum shear occurs at the left of P 2 and is 139,412 
pounds. By constructing the shear diagram, it is found that the 
shear passes from positive to negative at P 2 . This position of zero 

shear establishes the point of maximum 
moment. Computing the moment from 
the loads and reaction on the left 


Up 

i 

* s 

mum. 

•+ u ^ 

■* Lf U -*" 

~ 

gp 

m. 

/f 


gives 


4-7 X 130,588 = +914,116 
—4X 60,000 =-240,000 


Fig. 78. Cantilever Beam with 
Concentrated Loads 


+674,116 ft.-lb. 


Computing on the right gives 

4- 10X 139,412 = 4-1,394,120 

- 4X 80,000 = 320,000 

- 8 X 50,000 = 400,000 - 720,000 

4- 674,120 ft.-lb. 


Cantilever Beam. Fig. 78 represents a cantilever supporting 
the concentrated loads P, and P 2 . 

R = P t + P 2 = 30,000+40,000 = 70,000 # 

The maximum shear is 70,000 at the right of P. Zero shear is at 
the right of P 3 . 

The maximum bending moment is at P. It is 


-4X30,000=-120,000 
-9 X40,000 =-360,000 

-480,000 ft.-lb. 

Simple Beams on Two Supports and Projecting at Both Ends. 
Fig. 79 represents a beam resting on two supports and projecting 
beyond both of them. It supports concentrated loads as shown. 
The loads are 

P x = 15,000# 

P 2 = 15,000# 

P 8 = 15,000# 

P 4 = 15,000# 

P 6 = 15,000# 

P 8 = 30,000# 


Total load = 105,000# 















STEEL CONSTRUCTION 


87 


To determine the reaction R 2 , take moments about R t : 
0X15,000 (P 2 ) = 00,000 
4X15,000 (P 3 ) = 60,000 
8X15,000 (P 4 ) = 120,000 
12X15,000 (P 6 ) =180,000 
16X30,000 (P e ) =4S0,000 840,000 ft.-lb. 


- 4X15,000 (P x ) = 
Moment of reaction R 2 = 


- 60,000 
780,000 ft.-lb. 




Fig. 79. Overhanging Beam with Concentrated Loads Shear 
and Moment Diagrams 


r 2 


780,000 

12 


65,000 £ 


To determine the reaction P„ take moments about R 2 : 
0X15,000 (P 5 )= 00,000 
4X15,000 (P 4 )= 60,000 
8X15,000 (P 3 ) = 120,000 
12X15,000 (P 2 ) = 180,000 
16X 15,000 (P x ) =240,000 600,000 ft.-lb. 

- 4X30,000 (P 8 )= - 120,000 

Moment of reaction R t = 480,000 ft.-lb. 






















































































































































































































































88 


STEEL CONSTRUCTION 


Therefore 



480,000 

12 


= 40,000# 


The shear values are 

V t = 15,000 
F 2 = 10,000 
U 3 = 20,000 
V 4 = 30,000 

Zero shear occurs at P 3 . 

The bending moments are maximum negative at R x and R 2 and 
maximum positive at P 3 . Their values are 

at P, M= -4X15,000= - 60,000 ft.-lb. 

at P 2 M= -4X30,000= -120,000 ft.-lb. 


at P 3 M = < 


'+4X40,000 =+160,000 
-4X15,000=- 60,000 
. — 8X15,000 = — 120,000 — 20,000 ft.-lb. 


From the last result, it develops that the bending moment at P 3 is 
minimum negative (not considering the ends of the cantilevers) and 
not maximum positive. Hence there is no reversal of moment in 
this case. The moment diagram shows this. 


EXAMPLES FOR PRACTICE 

1. Solve the preceding case for the following loads: P,= 
10,000#; P 2 = 10,000#; P 3 = 15,000#; P 4 = 20,000#; P 6 = 20,000#; 
P 6 = 15,000#. Construct the shear and moment diagrams. 

2. What are the maximum shear and bending moment for a load 
of 40,000 pounds at the center of an 8-foot span? Of a 10-foot 
span? Of a 12-foot span? Of a 14-foot span? Of a 16-foot span? 
What is the ratio of the bending moments for the 8-foot and 16-foot 
spans? 

Compare these results with those from the second problem 
under uniformly distributed loads and note that the bending moments 
are the same though the uniformly distributed load is twice the 
concentrated load. 

3. Compute the shear and bending moment for two loads of 
40,000 pounds each, placed at the third points of a 16-foot span; at 
the quarter points. Compare with the preceding problem. 





STEEL CONSTRUCTION 


89 


p„ 


C 


ML 


p,*p t 'p 


<0 


4. A load at the center of a 20-foot span produces a bending 
moment of 200,000 foot-pounds. What is the load? 

5. Two equal loads at the 
quarter points of a 20-foot span 
produce a bending moment of 
100,000 foot-pounds. What are 
the loads? 

Combined Loads. Under Fi ‘ "■ Di * ,rib "’ 

“combined loads” are considered 

the combinations of uniformly distributed and concentrated loads, and 
of uniformly distributed loads on parts of spans. In computing 
moments in these cases, the uniformly distributed load may be con¬ 
sidered as concentrated at its center of gravity, Fig. 80, unless the 
center of moments is within the 
space occupied by the load; in 
which case the parts of the load 
to the right and to the left of the 
center of moments must be con¬ 
sidered as concentrated at their 
respective centers of gravity. 

Thus, if the center of moments 

is at /?! or R 2 , the concentrated load P is used; but if the center 



Fig 81. Simple Beam with Variable Load 


0 the concentrated loads P, and P 2 are used. 

the distributed load is variable instead 


of moments is at 
The same principle applies if 
of uniformly distributed, Fig. 81. 

Full Length Distributed Load 
and Concentrated Load. Fig. 82 
illustrates a beam with a uni¬ 
formly distributed load full 
length and a concentrated load, 
as shown. 

Total load = 10,000# (u.d.) 

+ 10,000# (con.) = 20,000# 

Moments about P, are 
10X10,000=100,000 
15X10,000 = 150,000 

250.000 ft.-lb. : 



Fig. 82. Simple Beam with Uniformly Distribu¬ 
ted Load over Entire Length and One 
Concentrated Load 



















































































































































'90 


STEEL CONSTRUCTION 


Therefore R 3 «= ^ = 12,500# 

/?, = 20,000-12,500 = 7500# 

Maximum shear is 12,500 #. Zero shear occurs under the 
load P. Hence this is the point of maximum bending moment. 
The bending moment computed on the right is 
+5 X 12,500 =+62,500 
—2gX5x500= — 6,250 

56,250 ft.-lb. 

The bending moment computed on the left is 
+ 15 X 7,500 = + 112,500 
- 7§X 15x500= — 56,250 



Fig. 83. Simple Beam with Two Rates of Uniformly Distributed Load 


Two Uniformly Distributed Loads Not Overlapping. Fig. 83 
illustrates a beam with one uniformly distributed load on part of its 
length and another load on the remainder, as shown. The total load 


on the beam is 


14 X 600 = 8400 
7X1000 = 7000 


Total load = 15,400# 






















































































































































































































































STEEL CONSTRUCTION 


91 


Moments about R t are 

7 X8400= 58,800 
17^ X 7000 = 122,500 

181,300 ft.-lb. 

Therefore i? 2 =l®l|00=8633# 

Moments about R 2 are 

3^x7000= 24,500 
14 XS400 = 117,600 

142,100 ft.-lb 

Therefore ^ = 142,100 

-4- 1 

R x +R 2 = 6767+8633 = 15,400 # 


Maximum shear is 8633. 


Zero shear occurs at a point 


6767 

600 


or 


11.28 feet to the right of R t . Hence this is the point of maximum 
bending moment. 

The bending moment computed on the right is 


+9.72X8633 = +83,913 

9 79 

-=^=X2.72X600=- 2220 

Li 

— 6.22X7000 =-43,540 -45,760 

’ +38,153 ft.-lb. 

The bending moment computed on the left is 
+ 11.28X6767 =+76,332 

_1L??X11.28X600= -38,166 

+38,166 ft.-lb. 

Two Distributed Loads and Concentrated Loads. Fig. 84 illus¬ 
trates a beam with one uniformly distributed load for part of its 
length, another load for the remainder, and a concentrated load as 
shown. The total load on the beam is 


u.d. 12X1,000 = 12,000 
u.d. 4X 500= 2,000 
concentrated = 10,000 


Total load — 24,000 # 













92 


STEEL CONSTRUCTION 


Moments about /?, are 



Fig. 84. Simple Beam with Mixed Loads 


6X12,000= 72,000 
12X10,000 = 120,000 
14 X 2,000= 28,000 


Therefore 


220,000 ft.-lb. 



220,000 

16 


13,750# 


Moments about R 2 are 

2X 2,000= 4,000 
4X10,000= 40,000 
10 X 12,000 = 120,000 

164,000 ft.-lb. 


Therefore R. = ^77 

16 





= 10,250# 

Maximum shear is 13,750#* 
Zero shear occurs at 10.25 feet 
from R r Hence this is the 
point of maximum bending mo¬ 
ment. 

The bending moment com¬ 
puted on the left is 

+ 10.25 X 10,250 =+105,062 
- 5.125X10,250=- 52,531 

52,531 

ft.-lb. 

This value is to be checked by 
computing the bending moment 
on the right. 


EXAMPLES FOR PRACTICE 

1 . Compute the bending moments for the loads illustrated in 
Fig. 85. Compare results with a uniformly distributed load. 

2 . A beam 20 feet long supports a load of 250 pounds on the 
first 5 feet, 400 pounds on the second 5 feet, and 350 pounds on the 
















































































































































































































STEEL CONSTRUCTION 


93 


remainder. What is the maximum shear? What is the position of 
the maximum bending moment? 

3. What is the bending moment on an I-beam 15"X42#X30 
feet long, due to its own weight and to a load of 14,000 pounds con¬ 
centrated at mid-span? 

Typical Loadings. Tabular Data. When the shear and the 
bending moment can be expressed in simple formulas, it is easier to 
compute from the formulas than from the detailed calculations just 
illustrated. Table II has been compiled fo^ this purpose. It gives 
the common arrangements of loading and the formulas for end reac¬ 
tions and maximum bending moment for each case. 

Column 1 gives diagrams of the arrangement of the loading. 

Columns 2 and 3 give the end reactions which, for all the cases 
given, are the same as the end shears. When the loading is sym¬ 
metrical, the reaction is the same at both ends and is one-half the 
total load. When not symmetrical, the values differ at the two 
ends and both are given. 

Column 4 gives the maximum bending moment. 

Column 5 gives the distance in feet from the left support to 
the point of maximum bending moment. 

The symbols used are: 

total uniformly distributed or variable loads in pounds 
single concentrated load in pounds 
span in feet 

distance from support to center of gravity of load on canti¬ 
lever beams 

bending moment in foot-pounds 
reaction at left support 
reaction at right support 

distance from left support to position of maximum bending 
moment 

Simple Loads. When a load on a simple beam is symmetrically 
placed, whether uniformly distributed or concentrated, the reac¬ 
tions are equal, and the maximum bending moment is at the center 
of the span. 

For a simple beam, irrespective of the manner of loading, the 
ma ximum bending moment and zero shear occur at the same point. 


W = 
P = 
L = 

4 = 

M = 

* 2 = 
x = 


94 STEEL CONSTRUCTION 

TABLE II 


Reactions and Bending Moments for Typical Loadings 



































































































STEEL CONSTRUCTION 

TABLE II—(Continued) 

Reactions and Bending Moments for Typical Loadings 


95 





































































































96 


STEEL CONSTRUCTION 


The point of zero shear is important only as the easiest means of 
locating the place of maximum bending moment. 

For a cantilever beam, irrespective of the manner of loading, the 
maximum bending moment and maximum shear occur at the sup¬ 
port. 

Illustrative Examples. To illustrate the use of Table II, assume 
a beam 18 feet long to be loaded from the left support to the middle 
at 320 pounds per lineal foot. 

W =9X320 =2880# 

F 1 = R 1 = fIF=fx2880 =2160# 

F 2 = /? 2 = * IF = ^ X2880 = 720# 

M =&WL =&X2880Xl8 = 7290 ft.-lb. 

Moving Loads. It is sometimes necessary to know what posi¬ 
tion of a moving load will produce the maximum bending moment in 
a beam. If it is a single concentrated load, the maximum occurs 
when the load is at the center of the span, as in item 16. Compare 
items 16, 17, and 19. If there are two concentrated loads, as the 
wheels of a traveling crane, the position producing the maximum is 
shown in item 23. As there indicated, one load is j D distant on 
one side of the center of the span and the other is f D distant on the 
other side. The maximum bending moment is at the load nearer 
to the center. 

Illustrative Example. Assume two crane wheels spaced 8 feet 
centers, each loaded with 10,000 pounds, span 20 feet, to find maxi¬ 
mum bending moment. From the formulas 

7?j = 8,000# and R 2 = 12,000#; A = 8 ft. 

Max. M = 8 X 8000 = 64,000 ft.-lb. 

Beam with Two or More Loadings. A beam may have two or 
more of the loadings illustrated. The respective reactions for the 
combined loads are the sums of the corresponding reactions for the 
separate loadings. This applies in all cases. The maximum bend¬ 
ing moment for the combined loads is the sum of the moments for 
the separate loadings, provided the positions of the maximums for 
the separate loadings are the same. Generally this condition occurs 
only when all the loads are symmetrical about the center of the 
span, or for cantilever beams. 


STEEL CONSTRUCTION 97 

EXAMPLES FOR PRACTICE 

1 . What is the bending moment of a concentrated load of 
89,000 pounds at the center of a span 21'-6" long? 

2 . What are the shear and bending moment of a load of 21,000 
pounds at the quarter point of a span 19 feet long? 

3. A beam is loaded at 750 pounds per lineal foot on the two 
end-thirds. What is the bending moment? 

4. A beam carries a uniformly distributed load of 18,000 
pounds and a center load of 9000 pounds. Span 16 feet. What 
are the reactions and maximum bending moment?' 

5. A crane girder has a span of 20 feet. The wheel load is 
30,000 pounds. The wheel base is 10 feet. What is the position of 
loads for maximum bending moment? What is the amount of the 
maximum bending moment? 

CALCULATION OF RESISTANCE 

Factors Considered. Having determined the shear and bending 
moment to which a beam is subjected, the next step, logically, is to 
determine the dimensions of the section which will resist them. 
The resistance to bending is first provided for, as this usually governs 
in the design of the rolled beam section. Then the shearing resist¬ 
ance is compared with the shearing stress to make sure that it is 
sufficient. To investigate the resisting moment in complete detail 
would require the following operations: 

(1) Assume maximum unit stress on extreme fiber 

(2) Assume section of beam, and compute its me lent of inertia 

(3) From these values compute the resisting moment of the 

assumed section 

(4) Compare this resisting moment with the bending moment 

(5) Repeat the operation until a resisting moment is found which 

equals or slightly exceeds the bending moment 

This procedure, with some additional steps, is followed in the 
case of riveted beams, but for roiled beams the tables in the hand¬ 
books and elsewhere give resisting moments and various other 
properties of the sections so that the operations are much simplified. 

Resisting Moment. The resisting moment of any beam is 
determined from the formula 

M = S- 

c 


98 


STEEL CONSTRUCTION 


as stated on p. 78 and demonstrated under Resisting Moment in 
“Strength of Materials” Part I. This formula may be changed to 
the form 

l = M 

c S 

which stated in words is 

moment of inertia _ resisting moment 

one-half the depth unit stress 


n. 


Section Modulus. In the expression just given - is called the 

, c 

section modulus,” (p. 39). Its values for I-beams, channels, and 
angles are given in the handbook. Since the resisting moment must 
be equal to or greater than the bending moment and, since the value 
of the unit stress has been established, the value of the section 
modulus can be computed and the section selected from the tables. 
For example, the allowable unit stress in bending on the extreme 
fiber is 16,000 pounds per square inch; assume a beam subjected 
to a bending moment of 100,000 foot-pounds; since the section 
modulus is in terms of inches, the bending moment must be expressed 
in inch-pounds and for this case becomes 1,200,000 inch-pounds; 
then the section modulus required is 

J_M _ 1,200,000 _ 

c S 16,000 “ 75 '° 


Referring to the tables for I-beams it is found that the section having 
the nearest higher value of the section modulus is* 

15* I 60# 

Expressed in simple words the operations are: 

(1) Multiply the bending moment of the beam by 12 to reduce it to inch-pounds. 

(2) Divide this by 16,000 to determine the required section modulus. 

(3) From the tables select a section whose section modulus is equal to or greater 

than the required value. 

Tabular Values for Resisting Moments. For a given unit stress 
each section has a definite resisting moment which is computed from 
the formula 

M=S- 

c 

The values of the resisting moment are not given in all of the hand- 




STEEL CONSTRUCTION 


99' 


books. They are given in Table III, based on a unit stress of 16,000 
pounds per square inch, and expressed in foot-pounds. This shortens 
the operation of selecting a section, it being necessary only to 
choose a section whose resisting moment is equal to or greater than 
the bending moment produced by the load on the beam. 

For example, assume a bending moment of 30,625 foot-pounds. 
Referring to Table III, the beam having the nearest higher resisting 
moment is 10" I 25$, whose resisting moment is 32,500 foot-pounds. 

If the load on the beam is uniformly distributed, the compu¬ 
tations may be still further shortened by means of tables given in 
the handbooks. These tables give the safe loads uniformly dis¬ 
tributed for various lengths of spans. The Carnegie handbook has 
formerly given these values for I-beams, channels, angles, tees, and 
zees in tons but in the 1913 edition they are given in thousands of 
pounds. The Cambria handbook gives the values for I-beams and 
channels only and expresses them in pounds. For example, a beam 
20 feet long supports a load of 700 pounds per lineal foot. The total 
load is 20X700 = 14,000$. From the tables the size of beam is 
found to be 10" I 30$. 

EXAMPLES FOR PRACTICE 

1 . Two angles are required to support a load of 4200 pounds 
uniformly distributed on a span of 6 feet. Determine the section, 
by means of the section modulus. 

2 . A channel having a span 12'-6" long is required to support 
a concentrated load of 17,900 pounds at the middle point. What 
section is required? 

3. Determine the sizes of beams required for the conditions 
given in the problems on p. 97. Use the simplest of the three 
methods given above, and check the results by one of the other 
methods. 

Application of Tables to Concentrated Loads. By careful 
study of the moment factors given in Table II, the designer can 
adapt the tables in the handbooks for uniformly distributed loads 
to other forms of loading. Thus a concentrated load at the center 
of a span produces the same bending moment as a uniformly dis¬ 
tributed load of twice the amount; then to use the table select a 
beam whose capacity is twice the amount of the concentrated load. 


100 


STEEL CONSTRUCTION 

TABLE III 
Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 

Moment 

of 

Inertia 

I 

Section 

Modulus 

J _ 

C 

Resisting 
Moment 
Based on 
Unit Stress 
of 16.000 
Lb. per 
Sq.Inch 

Shearing 
Resistance 
of Web 
at 10,000 
Lb. per 
Sq. Inch 

Strength 

of 

Standard 
End Con¬ 
nections 
American 
Bridge 
Co.. 1911 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-360 Span 

Extreme Length 
for Beams without 
Lateral Support 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 

When 
Loaded 
to Full 
Capacity 

When 
Loaded 
to Half 
Capacity 


(In.)« 

( In .)* 

Ft.-Lb. 

Pounds 

Pounds 

Ft. In. 

Ft. In. 

Ft. In. 

Ft In 

27 " I 83 # 

2888.6 

214 . 0 - 

285,300 

114,500 


54-0 

36-0 

12 - 6 

37-6 

24 " I 115 # 

2955.5 

246 3 

328,400 

180,000 

53,000 

48-0 

32-0 

13 - 4 

40-0 

110 

2883.5 

240.3 

320,400 

165,100 

it 

II 

It 

13 - 3 

39-0 

105 

2811.5 

234.3 

312,400 

150,000 

it 

II 

li 

13 - 1 

39-4 

100 

2380.3 

198.4 

264,500 

181,000 

it 

II 

44 

12 - 1 

36-3 

95 

2309.6 

192.5 

256,700 

166,100 

It 

II 

44 

12 - 0 

36-0 

90 

2239.1 

186.5 

248,800 

151,400 

it 

II 

II 

11-11 

35-8 

85 

2168.6 

180.7 

240,900 

136,800 

it 

II 

44 

11 - 9 

35-4 

80 

2087.9 

174.0 

232,000 

120,000 

it 

II 

14 

11 - 8 

35-0 

69 J 

1928.0 

160.7 

214,300 

93,600 

43,900 

II 

41 

11 - 8 

35-0 

21 'I 57 }# 

1227.5 

116.9 

155,900 

75,000 

33,400 

42-0 

28-0 

10-10 

32-6 

20 " I 100 # 

1655.8 

165.6 

220,800 

176,800 

44,200 

40-0 

26-8 

12 - 2 

36-5 

95 

1606.8 

160.7 

214,300 

162,000 

ii 

II 

14 

12 - 0 

36-1 

90 

1557.8 

158.5 

207,700 

147,400 

n 

II 

44 

11-11 

35-8 

85 

1508.7 

150.9 

201,200 

132,600 

u 

II 

H 

11 - 9 

35-4 

80 

1466.5 

146.7 

195,600 

120,000 

n 

II 

II 

11 - 8 

35-0 

75 

1268.9 

126.9 

169,200 

129,800 

a 

II 

It 

10 - 8 

32-0 

70 

1219.9 

122.0 

162,700 

115,000 

n. 

II 

II 

10 - 7 

31-8 

65 

1169.6 

117.0 

156,000 

100,000 

a 

It 

II 

10 - 5 

31-3 

18 'I 90 # 

1260.4 

140.0 

186,700 

145,300 

43,100 

36-0 

24-0 

12 - 1 

36 - 3 

85 

1220.7 

135.6 

180,800 

130,500 

n 

II 

44 

11-11 

35-10 

80 

1181.0 

131.2 

175,000 

115,900 

n 

II 

li 

11-10 

35 - 5 

75 

1141.3 

126.8 

169,100 

101,200 

n 

II 

It 

11 - 8 

35 - 0 

70 

921.3 

102.4 

136,500 

129,400 

a 

II 

II 

10 - 5 

31 - 4 

65 

881.5 

97.9 

130,500 

114,700 

it 

II 

44 

10 - 4 

30-11 

60 

841.8 

93.5 

124,700 

99,900 

u 

II 

II 

10 - 2 

30 - 6 

55 

795.6 

88.4 

117,900 

82,800 

a 

II 

44 

10 - 0 

30 - 0 

46 

733.2 

81.5 

108,700 

58,000 

30,200 

II 

44 

11 - 8 

35 - 0 

15 ' I 100 # 

900.5 

120.1 

160,100 

177,600 

35,400 

30-0 

20-0 

11 - 3 

33-10 

95 

872.9 

116.4 

155,200 

162,800 

<4 

II 

14 

11 - 1 

33 - 4 

90 

845.4 

112.7 

150,300 

148,000 

II 


44 

11 - 0 

32-11 

85 

817.8 

109.0 

145,300 

133,400 

li 

II 

44 

10 - 9 

32 - 4 

80 

795.5 

106.1 

141,500 

121 , .500 

II 

II 

44 

10 - 8 

32 - 0 

75 

691.2 

92.2 

122,900 

132,300 

II 

II 

44 

10 - 6 . 

31 - 5 

70 

663.6 

88.5 

118,000 

117,600 

II 

II 

44 

10 - 4 

31 - 0 

65 

636.0 

84.8 

113,100 

102,900 

II 

It 

44 

10 - 2 

30 - 6 

60 

609.0 

81.2 

108,300 

88,500 

II 

II 

44 

10 - 0 

30 - 0 

55 

511.0 

68.1 

90,800 

98,400 

II 

II 

44 

O - 7 

28 - 9 

50 

483.4 

64.5 

86,000 

83,700 

II 

II 

44 

9 - 5 

28 - 3 

45 

455.8 

60.8 

81,100 

69,000 

II 

tl 

44 

9 - 3 

27 - 9 

42 

441.7 

58.9 

78,500 

61,500 

II 

41 

44 

0- 2 

27 - 6 

36 

405.1 

54.1 

72,000 

43,400 

32,500 

44 

44 

0 - 2 

27 - 6 












































101 


STEEL CONSTRUCTION 

TABLE III (Continued) 
Strength of Beams 


I - Beams ; H - Sections ; Channels ; Angles ; and Tees 


SECTION 

Moment 

of 

Inertia 

I 

Section 

Modulus 

I 

c 

Resisting 
Moment 
Based on 
Unit Stress 
of 16.000 
Lb. per 
Sq. Inch 

Shearing 
Resistance 
of Web 
at 10,000 
Lb. per 
Sq. Inch 

Strength 

of 

Staodard 
End Con¬ 
nections 
American 
Bridge 
Co., 1911 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-360 Span 

Extreme Length 
for Beams without 
Lateral Support 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 

When 
Loaded 
to Full 
Capacity 

When 
Loaded 
to Half 
Capacity 


(In.) 4 

(In.) 3 

Ft.-Lb. 

Pounds 

Pounds 

Ft. In. 

Ft. In. 

Ft. In. 

Ft In. 

12 " I 55 # 

321.0 

53.5 

71,300 

98,600 

26,500 

24-0 

16-0 

9 - 4 

28 - 1 

50 

303.3 

50.6 

67,500 

83,900 

<4 

44 

44 

9 - 2 

27 - 5 

45 

285.7 

47.6 

63,500 

69,100 

44 

44 

44 

8-11 

26-10 

40 

268.9 

44.8 

59,700 

55,200 

44 

<4 

44 

8 - 9 

26 - 3 

35 

228.3 

38.0 

50,700 

52,300 

u 

44 

44 

8 - 6 

25 - 5 

311 

215.8 

36.0 

48,000 

42,000 

a 

44 

44 

8 - 4 

25 - 0 

27 } 

199.6 

33.3 

44,400 

38,200 

23,900 

44 

44 

8 -4 

25 - 0 

10 " I 40 # 

158.7 

31.7 

42,300 

74,900 

17,700 

20-0 

13-4 

8-6 

25-6 

35 

146.4 

29.3 

39,100 

60,200 

44 

44 

44 

8-3 

24-9 

30 

134.2 

26.8 

35,700 

45,500 

a 

44 

44 

8-0 

24-0 

25 

122.1 

24.4 

32,500 

31,000 

t ( 

44 

44 

7-9 

23-4 

22 

113.9 

22.8 

30,400 

23,200 

17,400 

44 

44 

7-9 

23-4 

‘ 9 " I 35 # 

111.8 

24.8 

33,100 

65,900 

17,700 

18-0 

12-0 

7-11 

23-10 

30 

101.9 

22.6 

30,100 

51,200 

44 

44 

44 

7 - 8 

23 - 0 

25 

91.9 

20.4 

27,200 

36,500 

44 

44 

44 

7 - 5 

22 - 3 

21 

84.9 

18.9 

25,200 

26,100 

44 

44 

44 

7 - 3 

21 - 8 

8 " I 25 

68.4 

17.1 

22,800 

43,300 

17,700 

16-0 

10-8 

7 - 1 

21 - 4 

23 

64.5 

16.1 

21,400 

35,900 

44 

44 

44 

7 - 0 

20-11 

20 5 

60.6 

15.1 

20,100 

28,600 

44 

44 

44 

6-10 

20 - 5 

18 

56.9 

14.2 

18,900 

21,600 

a 

44 

44 

6 - 8 

20 - 0 

171 

58.3 

14.6 

19,500 

16,800 

15,800 

44 

44 

7 - 3 

21 - 8 

7 " I 20 # 

42.2 

12.1 

16,100 

32,100 

17,700 

14-0 

9-4 

6-5 

19 - 4 

171 

39.2 

11.2 

14,900 

24,700 

44 

44 

44 

6-3 

18-10 

15 

36.2 

10.4 

13,900 

17,500 

44 

44 

44 

6-1 

18 - 4 

6 " I 17 |# 

26.2 

8.7 

11,600 

28,500 

8,800 

12-0 

8-0 

7-2 

21-5 

141 

24.0 

8.0 

10,700 

21,100 

44 

44 

44 

5-9 

17-3 

121 

21.8 

7.3 

9,700 

13,800 

8,600 

44 

44 

5-7 

16-8 

5 " I 141 # 

15.2 

6.1 

8,100 

25,200 

8,800 

10-0 

6-8 

5-6 

16-6 

121 

13.6 

5.4 

7,200 

17,800 

44 

44 

44 

5-3 

15-9 

91 

12.1 

4.8 

6,400 

10,500 

7,900 

44 

44 

5-0 

15-0 

4 ' I 101 # 

7.1 

3.6 

4,800 

16,400 

8,800 

8-0 

5-4 

4-10 

14-5 

91 

6.7 

3.4 

4,500 

13,500 

44 

44 

44 

4 - 8 

14-0 

. 81 

6.4 

3.2 

4,300 

10,500 

44 

44 

44 

4 - 7 

13-8 

71 

6.0 

3.0 

4,000 

7,600 

7,100 

44 

44 

4 - 5 

13-4 

3 " I 71 # 

2.9 

1.9 

2,500 

10,800 

8,800 

6-0 

4-0 

4 - ~ 2 ~ 

12-7 

61 

2.7 

1.8 

2,400 

7,900 

44 

44 

44 

4 - 0 

12-1 

51 

2.5 

1.7 

2,270 

5,100 

6,400 

44 

44 

3-11 

11-8 

H - 8 "- 34 . 0 # 

115.4 

28.9 

38,500 

30,000 

— 

13-4 

10-8 

— 

— 

6 "- 23.8 

45.1 

15.0 

20,000 

18,800 

— 

12-0 

8-0 

— 

— 

5 '- 18.7 

23.8 

9.5 

12,700 

15,600 

— 

10-0 

6-8 

— 

— 

4"-13 6 

10.7 

5.3 

7,100 

12,500 

- 1 

8-0 

5-4 

— 

— 

















































102 


STEEL CONSTRUCTION 

TABLE III (Continued) 
Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 

Moment 

of 

Inertia 

I 

Section 

Modulus 

X 

0 

Resisting 
Moment 
Based on 
Unit Stress 
of 16,000 
Lb. per 
Sq. Inch 

Shearing 
Resistance 
of Web' 
at 10,000 
Lb. per 
■ .Sq.Inch 

Strength 

of 

Standard 
End Con¬ 
nections 
American 
Bridge 
Co., 1911 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-360 Span 

Extreme Length 
for Beams without 
Lateral Support 

For 

Uniformly 
Distrib¬ 
uted Loac 

For 

Center 

Load 

When 
Loaded 
to Full 
Capacity 

When 
Loaded 
to Half 
Capacity 


fin,)* 

(In.) 3 

Ft.-Lb. 

Pounds 

Pounds 

Ft. In. 

Ft. In. 

Ft. In. 

Ft. In. 

15" C 55# 

430.2 

57.4 

76,500 

122,700 

35)400 

30-0 

20-0 

6 - 4 

19-1 

40 

402.7 

53.7 

71,600 

108,000 

ll 

u 

ll 

6 - 2 

18-6 

45 

375.1 

50.0 

66,700 

93,300 

Jt 

It 

It 

6 - 0 

18-1 

40 

347.5 

46.3 

61,700 

78,600 

ll 

ll 

it 

5-11 

17-7 

35 

320.0 

42.7 

56,900 

63,900 

ll 

ll 

It 

5- 9 

17-2 

33 

312.6 

41.7 

55,600 

60,000 

It 

ti 

ll 

5- 8 

17-0 ' 

12" C 40# 

197.0 

32.8 

43,700 

91,000 

26,500 

24-0 

16-0 

5- 8 

17- 1 

35 

179.3 

29.9 

39,900 

76,300 

ll 

It 

ll 

5- 6 

16- 6 

30 

161.7 

26.9 

35,900 

61,600 

It 

ti • 

ll 

5- 3 

15-10 

25 

144.0 

24.0 

32,000 

46,800 

n 

ll 

ll 

5- 1 

15- 3 

20i 

128.1 

21.4 * 

28,500 

33,600 

26,200 

ll 

it 

4-11 

14- 8 

10" C 35# 

115.5 

23.1 

30,800 

82',300 

17,700 

20-0 

13-4 

5- 4 

15-11 

30 

103.2 

20.6 

27,500 

67,600 

' ll 

It 

ll 

5- 1 

15- 2 

25 

91.0 

18.2 

24,300 

52,900 

u 

It 

U 

4-10 

14- 5 

20 

78.7 

15.7 

20,900 

38,200 

u 

It 

It 

4- 7 

13- 9 

15 

66.9 

13.4 

17,900 

24,000 

it 

ll 

It 

4- 4 

13- 0 

9" C 25# 

70.7 

15.7 

20,900 

55,400 

17,700 

18-0 

12-0 

4-8 

14-1 

20 

60.8 

13.5 

18,000 

40,700 

ll 

ll 

ll 

4-5 

13-3 

15 

50.9 

11.3 

15,100 

25,900 

It 

ll 

ll 

4-2 

12-5 

13* 

47.3 

10.5 

14,000 

20,700 

17,200 

ll 

ll 

4-1 

12-2 

8" E 21*# 

47.8 

11.9 

15,900 

46,600 

17,700 

16-0 

10-8 

4- 4 

13-1 

18* 

43.8 

11.0 

14,700 

39,200 

ll 

ll 

It 

4- 3 

12-8 

16* 

39.9 

10.0 

13,300 

31,900 

tt 

ll 

ll 

4- 1 

12-2 

13* 

36.0 

9.0 

12,000 

24,600 

n 

ll 

It 

3-11 

11-9 

11* 

32.3 

8.1 

10,800 

17,600 

16,500. 

ll 

it 

3- 9 

11-4 

7" C 19*# 

33.2 

9.5 

12,700 

44,300 

17,700 

14-0 

9-4 

4- 2 

12-7 

18* 

30.2 

8.6 

11,500 

37,000 

ll 

ll 

It 

4- 0 

12-0 

14* 

27.2 

7.8 

10,400 

29,600 

ll 

ll 

ll 

3-=40 

11-6 

12* 

24.2 

6.9 

9,200 

22,300 

ll 

It 

ll 

3- 8 

11-0 

9* 

21.1 

6.0 

8,000 

14,700 

15,800 

It 

ll 

3- 6 

10-5 

6 " C 15*# 

19.5 

6.5 

8,700 

33,800 

8,800 

12-0 

8-0 

3-10 

11- 5 

13 

17.3 

5.8 

7,700 

26,400 

It 

ll 

ll 

3- 7 

10-10 

10 * 

15.1 

5.0 

6,700 

19,100 

ll 

ll 

ll 

3- 5 

10 - 2 

8 

13.0 

4.3 

5,700 

12,000 

7,500 

It 

It 

3- 2 

9- 7 

5" E 11*# 

10.4 

4.2 

5,600 

23,800 

8,800 

10-0 

6-8 

3r 5 

10-2 

9 

8.9 

3.5 

4,700 

16,500 

ll 

It 

It 

3- 2 

9-5 

6* 

7.4 

3.0 

4,000 

9,500 

7,100 

ll 

It 

2-11 

8-9 

4" C 7*# 

4.6 

2.3 

3,100 

12,000 

8,800 

8-0 

5-4 

2-10 

8 - 7 

6* 

4.2 

2.1 

2,800 

10,100 

ll 

tt 

It 

2- 9 

8 - 3 

5* 

3.8 

1.9 

2,500 

7,200 

6,800 

ll 

It 

2 - 8 

7-11 

3" E 6 # 

2.1 

1.4 

1,870 

10,900 

8,800 

.6-0 

4-0 

■ 2-8 

8-0 

5 

1.8 

1.2 

1,600 

7,900 

ll ' 

It 

U 

2-6 

7-6 

4 

1.6 

1.1 

41,70 

5,100 

6,400 

a 

it 

2-4 

7-1 


















































103 


STEEL CONSTRUCTION 

TABLE III (Continued) 
Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 

Mom¬ 
ent of 
Inertia 

I 

Sec¬ 

tion 

Modu¬ 

lus 

2 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb. per 
Sq. Inch 

Extreme length 
for Deflection 
for Plastered 
Ceilings, Limit 
1-480 Span 

SECTION 

Mom¬ 
ent of 
Inertia 

I 

Sec¬ 

tion 

Modu¬ 

lus 

X 

e 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16.000 
Lb. per 
Sq.Inch 

Extreme length 
for Deflection 
for Plastered 
Ceilings, Limit 
1-480 Span 

ForUn- 

iformly 

Distrib¬ 

uted 

Load 

For 

Center 

Load 

For Un¬ 
iformly 
Distrib¬ 
uted 
Load 

For 

Center 

Load 


(InJ< 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 


(In.) 4 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

L- 8 x 8 xli 

97.97 

17.53 

23,400 

•17-0 

11-0 

L-3jx33X^ 

3.99 

1.65 

2,200 

7-0 

4-9 

Ire 

93.53 

16.67 

22,200 

ii 

it 

i 

3.64 

1.49 

1,990 

ft 

it 

1 

88.98 

15.80 

21,100 

it 

ii 

Te 

3.26 

1.32 

1,760 

ii 

it 

H 

S4.33 

14.91 

19,900 

a 

it 

I 

2.87 

1.15 

1,530 

ii 

ti 

7 

79.58 

14.01 

18,700 

it 

ii 

R 

2.45 

0.98 

1,310 

ii 

a 

rl 

74.71 

13.11 

17,500 

n 

ii 

L-3x3x R 

2.81 

1.40 

1,870 

6-0 

4-0 

3 

69.74 

12.18 

16,200 

u 

it 

- 5 

8 

2.62 

1.30 

1,730 

tt 

ii 

11 

64.64 

11.25 

15,000 

a 

it 

9 

16 

2.43 

1.19 

1,590 

ti 

it 

5 

59.42 

10.30 

13,700 

u 

it 

1 

5 

2.22 

1.07 

1,430 

tt 

tt 

9 

54.09 

9.34 

12,500 

a 

ii 

7 

16 

1.99 

0 95 

1,270 

tt 

tt 

i 

48.63 

8.37 

11,200 

a 

ti 

3 

8 

1.76 

0.83 

1,110 

tt 

ii 

L- 6 x 6 xl 

35.46 

8.57 

11,400 

12-6 

8-6 

_5_ 

16 

1.51 

0.71 

950 

it 

ii 

tt 

33.72 

8.11 

10,800 

it 

it 

I 

4 

1.24 

0 58 

770 

ti 

it 

7 

31.92 

7.64 

10,200 

t ( 

tt 

L-2|x2jX5 

1.67 

0.89 

1,190 

5-9 

3-9 

13 

30.06 

7 15 

9,500 

it 

tt 

7 

16 

1.51 

0.79 

1,050 

it 

n 

3 

28 15 

6.66 

8,900 

ti 

ii 

3 

8 

1 33 

0.69 

920 

it 

it 

11 

26 IP 

6 17 

8,200 

it 

ti 

R 

1.15 

0.59 

790 

tt 

it 

5 

24 16 

5.66 

7,500 

it 

it 


0.93 

0 48 

640 

it 

a 

9 

22.07 

5.14 

6,800 

tt 

tt 

L-2R2RR 

1.34 

0 80 

1,070 

5-0 

3-4 

h 

19.91 

4.61 

6,100 

a 

tt 

1 

2 

1.23 

0.73 

970 

it 

ii 

7 

17 68 

4.07 

5,400 

tt 

ii 

7 

16 

1.11 

0.65 

870 

ti 

it 

3 

15.39 

3.53 

4,700 

tt 

it / 

3 

8 

0.98 

0.57 

760 

ti 

ii 

L-5x5xl 

19.64 

5.80 

7,700 

10-6 

7-0 

R 

0.85 

0 48 

640 

ti 

ii 

rl 

18.71 

5.49 

7,300 

a 

it 

X 

4 

0.70 

0.40 

530 

it 

tt 

7 

17 75 

5.17 

6,900 

tt 

it 

A 

0.55 

0.30 

400 

ti 

ti 

rl 

16.77 

4.85 

6,500 

a 

it 

L-2jX2jX5 

0.87 

0.58 

770 

4-6 

3-0 

3 

15.74 

4.53 

6,000 

tt 

tt 

R 

0.79 

0.52 

690 

tt 

tt 

R 

14.68 

4.20 

5,600 

a 

it 

3 

8 

0.70 

0.45 

600 

tt 

it 

I 

13.58 

3.86 

5,100 

ti 

tt 

1 6 

0.61 

0.39 

520 

ti 

tt 

Ts 

12.44 

3.51 

4,700 

a 

tt 

1 

4 

0.51 

0.32 

430 

ti 

it 

1 

11.25 

3.15 

4,200 

a 

ti 

.-3_ 

■ l 6 

0.39 

0.24 

320 

ii 

a 

* 

10.02 

2.79 

3,700 

a 

tt 

L-2x2x5 

0.59 

0.45 

600 

4-0 

2-9 

3 

8.74 

2.42 

3,200 

a 

it 

Te 

0.54 

0.40 

530 

a 

it 

L-4x4x 5 

8.5P 

3.20 

4,300 

8-3 

5-6 

3 

8 

0.48 

0.35 

470 

a 

a 

11 

8.14 

3.01 

4,000 

it 

tt 

_ 5 _ 

16 

0.42 

0.30 

400 

a 

ti 

3 

7.67 

2.81 

3,700 

ll 

it 

X 

4 

0.35 

0.25 

330 

a 

a 

R 

7.17 

2.61 

3,500 

ti 

it 

R 

0.28 

0.19 

250 

a 

a 

5 

6.66 

2.40 

3,200 

ii 

tt 







Te 

6.12 

2.19 

2,900 

it 

ii 







h 

5.56 

1.97 

2,600 

tt 

tt 








4.97 

1.75 

2,300 

it 

a 







| 

4.36 

1.52 

2,000 

ti 

n 







.R 

3.71 

1.29 

1,700 

li 

a 







L-3|x3|xi 

5.53 

2.39 

3,200 

7-0 

4-9 


' 





R 

5.25 

2.25 

3,000 

ii 

ii 







1 

4.96 

2.11 

2,800 

ti 

it 







R 

4.65 

1.96 

2,600 

it 

it 







L 

4.33 

1.81 

2,400 

ti 

H 








































104 


STEEL CONSTRUCTION 

• TABLE III (Continued) 

Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 




LONG 

LEG VERTICAL 


SHORT LEG VERTICAL 


Moment 

Section 

Resisting 

Moment 

Extreme Length 
for Deflection for 
Plastered Ceilings 

Moment 

Section 

Resisting 

Moment 

Extreme Length 
for Deflection for 
Plastered Ceilings 

SECTION 

of 

Modulus 

Unit 

Limit 1-360 Span 

of 

Modulus 

Unit 

Limit 1-360 Span 


I 

0 

Stress 
of 16,000 
Lb. per 
Sq.Inch 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 

I 

I 

c 

Stress 
of 16,000 
Lb. per 
Sq.Inch 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 


(In.) 4 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

(In.) 4 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

L-8 x 6 x 1 

80.78 

15.11 

20,100 

16-3 

10-9 

38.78 

8.92 

11,900 

13-3 

8-9 

1 5 
T5 

76.59 

14.27 

19,000 

II 

II 

36.85 

8.43 

11,200 

II 

II 

1 

72.32 

13.41 

17,900 

14 

II 

34.86 

7.94 

10,600 

II 

II 

H 

67.92 

12.55 

16,700 

u 

II 

32.82 

7.44 

9,900 

II 

II 

3 

4 

63.42 

11.67 

15,600 

n 

II 

30.72 

6.92 

9,200 

II 

II 

11 
1 6 

58.82 

10.77 

14,400 

ii 

II 

28.56 

6.40 

8,500 

II 

II 

5 

8 

54.10 

9.87 

13,200 

ii 

II 

26.33 

5.88 

7,800 

II 

II 

9 

1 6 

49.26 

8.95 

11,900 

ii 

II 

24.04 

5.34 

7,100 

l.l 

II 

1 

2 

44.31 

8.02 

10,700 

ii 

II 

21.68 

4.79 

6,400 

II 

II 

L-7x3)xl 

45.37 

10.58 

14,100 

12-3 

8-9 

7.53 

2.96 

3,900 

7-9 

5-3 

R 

43.13 

10.00 

13,300 

II 

II 

7.18 

2.80 

3,700 

II 

II 

g 

40.82 

9.42 

12,600 

II 

II 

6.83 

2.64 

3,500 

II 

II 

H 

38.45 

8.82 

11,800 

l« 

II 

6.46 

2.48 

3,300 

II 

II 

3 

4 

35.99 

8.22 

11,000 

II 

II 

6.08 

2.31 

3,100 

II 

II 

11 

16 

33.47 

7.60 

10,100 

II 

II 

5.69 

2.14 

2,900 

II 

II 

5 

8 

30.86 

6.97 

9,300 

-II 

II 

5.28 

1.97 

2,600 

II 

II 

A 

28.18 

6.33 

8,400 

II 

II 

4.86 

1.80 

2,400 

II 

II 

1 

2 

25.41 

5.68 

7,600 

II 

II 

4.41 

1.62 

2,200 

II 

II 

7 

16 

22.56 

5.01 

6,700 

II 

II 

3.95 

1.47 

1,960 

II 

II 

L-6 x 4 x 1 

30.75 

8.02 

10,700 

11-9 

7-9 

10.75 

3.79 

5,000 

8-6 

5-9 

1 5 
16 

29.26 

7.59 

10,100 

II 

II 

10.26 

3.59 

4,800 

II 

II 

7 

8 

27.73 

7.15 

9,500 

II 

II 

9.75 

3.39 

4,500 

II 

II 

13 

16 

26.15 

6.70 

8,900 

II 

II 

9 23 

3.18 

4,200 

II 

II 

3 

4 

24.51 

6.25 

8,300 

II 

II 

8.68 

2.97 

4,000 

II 

II 

1 1 
16 

22.82 

5.78 

7,700 

II 

II 

8.11 

2.76 

3,700 

II 

II 

5 

8 

21.07 

5.31 

7,100 

II 

II 

7.52 

2.54 

3,400 

II 


16 

19.26 

4.83 

6,400 

II 

II 

6.91 

2.31 

3,100 

II 

II 

1 

2 

17.40 

4.33 

5,800 

II 

II 

6.27 

2.08 

2,800 

II 

II 

JL 

16 

15.46 

3.83 

5,100 

II 

II 

5.60 

1.85 

2,500 

II 

II 

3 

'8 

13.47 

3.32 

4,400 

II 

II 

4.90 

1.60 

2,100 

II 

II 

L-6x3|xl 

29.24 

7.83 

10,400 

11-8 

7-9 

7.21 

2.90 

3,900 

7-9 

5-3 

15 

16 

27.84 

7.41 

9,900 

II 

II 

6.88 

2.74 

3,700 

II 

II 

7 

8 

26.38 

6.98 

9.300 

II 

II 

6.55 

2.59 

3,500 

II 

II 

1 3 
16 

24.89 

6.55 

8,700 

II 

II 

6.20 

2.43 

3,200 

II 

II 

3 

4 

23.34 

6.10 

8,100 

II 

II 

5.84 

2.27 

3,000 

II 

II 

11 
16 

21.74 

5.65 

7,500 

II 

II 

5.47 

2.11 

2,800 

II 

II 

5 

8 

20.08 

5.19 

6,900 

II 

II 

5.08 

1.94 

2,600 

II 

II 

A 

18.37 

4.72 

6,300 

II 

II 

4.67 

1.77 

2,400 

II 

II 

1 

2 

16.59 

4.24 

5,700 

II 

II 

4.25 

1.59 

2,100 

II 

II 

7 

16 

14.76 

3.75 

5,000 

II 

II 

3.81 

1.41 

1,880 

II 

II 

3 

8 

12.86 

3.25 

4,300 

II 

II 

3.34 

1.23 

1,640 

II 

II 

L-5x4x 1 

16.42 

4.99 

6,700 

10-0 

6-8 

9.23 

3.31 

4,500 

8-6 

5-9 

11 

16 

15.54 

4.69 

6,300 

II 

II 

8.74 

3.11 

4,100 

II 

II 

3 

4 

14.60 

4.37 

5,800 

II 

II 

8.23 

2.90 

3,900 

II 

II 

11 
16 

13.62 

4.05 

5,400 

II 

II 

7.70 

2.69 

3,600 

II 

II 

5 

1 

12.61 

3.73 

5.000 

II 

II 

7.14 

2.48 

3,300 

II 

. II 

























































105 


STEEL CONSTRUCTION 

TABLE III (Continued) 
Strength of Beams 


X-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 


LONG 

LEG VERTICAL 


SHORT LEG VERTICAL 

Moment 

of 

Inertia 

I 

Section 

Modulus 

_I_ 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb. per 
Sq. Inch 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-480 Span 

Moment 

of 

Inertia 

1 

Section 

Modulus 

J_ 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb. per 
Sq.Inch 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-480 Span 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 


(In.) 4 

(In.) 3 

Ft-Lb. 

Ft In. 

Ft. In. 

(In.) 4 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

L-5 x 4 X ft 

11.55 

3.39 

4,500 

10-0 

6-8 

6.56 

2.26 

3,100 

8-6 

5-9 

h 

10.46 

3.05 

4,100 

t ( 

4 4 

5.96 

2.04 

2,700 

44 

44 

ft 

9.32 

2.70 

3,600 

4 « 

44 

5.32 

1.81 

2,400 

44 

44 

3 

8 

8.14 

2.34 

3,100 

14 

14 

4.67 

1.57 

2,100 

44 

44 

L-5x3R l 

15.67 

4.88 

6,500 

9-9 

6-6 

6.21 

2.52 

3,400 

7-6 

5-0 

n 

14.81 

4.58 

6,100 

44 

4 4 

5.89 

2.37 

3,200 

44 

44 

3 

4 

13.92 

4.28 

5,700 

1 4 

44 

5.55 

2.22 

3,000 

44 

44 

1 1 
16 

12.99 

3.97 

5,300 

<4 

44 

5.20 

2.06 

2,700 

44 

44 

5 

12 03 

3.65 

4,900 

• 4 

44 

4.83 

1.90 

2,500 

44 

44 

ft 

11.03 

3.32 

4,400 

• 4 

44 

4.45 

1.73 

2,300 

44 

44 

I 

9.99 

2.99 

4,000 

44 

44 

4.05 

1.56 

2,100 

44 

44 

T6 

8.90 

2.64 

3,500 

“ 3 

44 

3.63 ' 

1.39 

1,850 

44 

44 

3 

7.78 

2.29 

3,100 

44 

44 

3.18 

1.21 

1,610 

44 

44 

ft 

6.60 

1.94 

2,600 

44 

44 

2.72 

1.02 

1,360 

44 

44 

L- 5 x 3 x R 

13.98 

4.45 

5,900 

9-8 

6-6 

3.71 

1.74 

2,300 

6-8 

4-6 

3 

13.15 

4.16 

5,500 

44 

“ 

3.51 

1.63 

2,200 

44 

44 

UL 

12.28 

3.86 

5,100 

44 

4 4 

3.29 

1.51 

2,000 

44 

44 

5 

11.37 

3.55 

4,700 

44 

44 

3.06 

1.39 

1,850 

44 

44 


10.43 

3.23 

4,300 

44 

44 

2.83 

1.27 

1,690 

44 

44 

h 

9.45 

2.91 

3,900 

44 

4 4 

2.58 

1.15 

1,530 

44 

44 

re 

8.43 

2.58 

3,400 

44 

<4 

2.32 

1.02 

1,360 

44 

44 

1 

7.37 

2.24 

3.000 

44 

44 

2.04 

0.89 

1,190 

44 

44 

ft 

6.26 

1.89 

2,500 

44 

44 

1.75 

0.75 

1,000 

44 

44 

L-4R3x R 

10.33 

3.62 

4,800 

8-9 

5-9 

3.60 

1.71 

2,300 

6-6 

4-4 

3 

7 

9.73 

3.38 

4,500 

44 

4 4 

3.40 

1.60 

2,100 



H 

9.10 

3.14 

4,200 

44 

44 

3.19 

1.49 

1,990 

4 4 

44 

I 

8.44 

2.89 

3,900 

44 

44 

2.98 

1.37 

1,830 

44 



7.75 

2.64 

3,500 

44 

44 

2.75 

1.25 

1,670 



r 

7.04 

2-37 

3,200 

44 

44 

2.51 

1.13 

1.510 

44 

44 

T 6 

6.29 

2.10 

2,800 

44 

41 

2.25 

1.01 

1,350 

44 


I 

5.50 

1.83 

2,400 

44 

44 

1 98 

0.88 

1,180 

44 


ft 

4.69 

1.54 

2,100 

44 

44 

1.73 

0.76 

1,010 

44 

44 

L-4x3jX R 

7.77 

2.92 

3,900 

8-0 

5-6 

5.49 

2.30 

3,100 

7-6 

5-0 


7.32 

2.75 

3,700 

44 

44 

5.18 

2.15 

2,900 



u 

6.86 

2.56 

3,400 

44 

44 

4.86 

2.00 

2,700 



\ 

6.37 

2.35 

3,100 

44 

44 

4.52 

1.84 

2,500 



ft 

5.86 

2.15 

2,900 

44 

44 

4.17 

1.68 

2,200 

44 


1 

5.32 

1.93 

2,600 

44 

44 

3.79 

1.52 

2,000 



ft 

4.76 

1.72 

2,300 

44 

44 

3.40 

1.35 

1,800 



f 

4.18 

1.50 

2,000 

44 

44 

2.99 

1.18 

1,570 



ft 

3.56 

1.26 

1,680 

44 

44 

2 59 

1.01 

1,350 



L-4x3x R 

7.34 

2.87 

3,800 

8-0 

5-4 

3.47 

1.68 

2,200 

6-6 

4-4 


6.93 

2.68 

3,600 

44 

44 

3.28 

1.57 

2,100 



R 

6.49 

2.49 

3,300 

44 

44 

3.08 

1.46 

1,950 



P 

6.03 

2.30 

3,100 

44 

44 

2.87 

1.35 

1,800 



_ft 

5.55 

2.09 

2,800 

44 

44 

2.66 

1.23 

1,640 










































































106 


STEEL CONSTRUCTION 

TABLE III (Cdntinued) 
Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 

LONG LEG VERTICAL 

SHORT LEG VERTICAL 

Moment 

of 

Inertia 

I 

Section 

Modulus 

± 

c 

Resisting 
.Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb. per 
Sq. Inch 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-480 Span 

Moment 

of 

Inertia 

I 

Section 

Modulus 

JL 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb. per 
Sq.Inch 

Extreme Length 
for Deflection for 
Plastered Ceilings 
Limit 1-480 Span 

For 

Uniformly 
Distrib¬ 
uted Loac 

For 

Center 

Load 

For 

Uniformly 
Distrib¬ 
uted Load 

For 

Center 

Load 


(InJl 

(In.) 3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

(In.) < 

(In.)3 

Ft.-Lb. 

Ft. In. 

Ft. In. 

L-4x3x 3 

5.05 

1.89 

2,500 

8-0 

5-4 

2.42 

1.12 

1,490 

6-6 

4-4 


4.52 

1.68 

2,200 

44 

44 

2.18 

0.99 

1,320 

a 

44 

3 

I 

3.96 

1.46 

1,940 

44 

44 

.1.92 

0.87 

1,160 

a 

44 

A 

3.38 

1.23 

1,640 

it 

ii 

1.65 

0.74 

990 

a 

44 

L-35x3xji 

4.98 

2.20 

2,900 

7-0 

4-9 

3.33 

1.65 

2,200 

6-4 

4-3 

3 

4 

4.70 

2.05 

2,700 

a 

44 

3.15 

1.54 

2,100 

44 

44 

tt 

4.41 

1.91 

2,500 

a 

44 

2.96 

1.44 

1,920 

44 

44 

£ 

8 

4.11 

1.76 

2,300 

it 

44 

2.76 

1.33 

1,770 

44 

44 

9 

1 6 

3.79 

1.61 

2,100 

n 

44 

2.55 

1.21 

1,610 

44 

44 

* 

3.45 

1.45 

1,930 

tt 

ii 

2.33 

1.10 

1,470 

it 

44 

tV 

3.10 

1.29 

1,720 

tt 

tt 

2.09 

0.98 

1,310 

it 

44 

3 

8 

2.72 

1.13 

1,510 

n 

ii 

1.85 

0.85 

1,130 

it 

44 

A 

2.33 

0.96 

1,280 

tt 

it 

1.58 

0.72 

960 

H 

44 

L-3*x2*xH 

4.13 

1.85 

2,500 

6-4 

4-6 

1.72 

0.99 

1,320 

5-4 

3-6 

5 

6 

3.85 

1.71 

2,300 

it, 

44 

1.61 

0.92 

1,230 

44 

44 

16 

3.55 

1.56 

2,100 

tt 

44 

1.49 

0.84 

1,120 

44 

41 

1 

2 

3.24 

1.41 

1,880 

tt 

44 

1.36 

0.76 

1,010 

ii 

44 

7 

T 6 

2.91 

1.26 

1,680 

ii 

44 

1.23 

0.68 

910 

Ii 

44 

3 

8 

2.56 

1.09 

1,450 

it 

44 

1.09 

0.59 

790 

H 

44 

5 

16 

2.19 

0.93 

1,240 

it 

44 

0.94 

0.50 

670 

ii 

44 


1.80 

0.75 

1,000 

It 

44 

0.78 

0.41 

550 

44 

4 4 

L-3{x2x A 

2.64 

1.30 

1,730 

6-4 

4-3 

0.75 

0.53 

710 

4-4 

3-0 

5 

2.42 

1.17 

1,560 

tt 

44 

0.69 

0.48 

640 

44 

44 

T 6 

2.18 

1.05 

1,400 

ii 

44 

0 62 

0.43 

570 

44 

44 

3 

8 

1.92 

0.91 

1,210 

tt 

44 

0.55 

0.37 

490 

44 

44 

A 

1.65 

0.77 

1,030 

it 

4 4 

0.48 

0.32 

430 

44 

44 

1 

4 

1.36 

0.63 

840 

It 

it 

0.40 

0.26. 

350 

44 

44 

L-3x23X & 

2.28 

1.15 

1,530 

6-0 

4-0 

1 42 

0.82 

1,090 

4-4 

3-6 

1 

2 

2 08 

1.04 

1,390 

tt 

44 

1.30 

0.74 

990 

4 4 

44 

JL 

1 6 

1 88 

0.93 

1,240 

it 

4 1 

1.18 

066 

880 

41 

44 

3 

8 

1.66 

081 

1,080 

11 

44 

1.04 

0.58 

770 

44 

44 , 

A 

1.42 

0.69 

920 

11 

it 

0.90 

0.49 

650 

14 

44 

I 

4 

1.17 

0.56 

750 

it 

4 < 

0.74 

0.40 

530 

44 

44 

L-3x2x 3 

1.92 

1.00 

1,330 

5-9 

3-9 

0.67 

0.47 

630 

4-4 

3-0 

T 6 

1.73 

0.89 

1,190 

it 

44 

0.61 

0.42 

560 

44 

44 

1 

1.53 

0.78 

1,040 

tt 

44 

0.54 

0.37 

490 

44 

44 

A 

1.32 

0.66 

880 

ii 

44 

0 47 

0.32 

430 

44 

44 

$ 

1.09 

0.54 

720 

ii 

44 

0.39 

0.25 

330 

44 

44 ' 

L-2|x2x £ 

1.14 

0.70 

930 

5-0 

3-4 

0.64 

0.46 

610 

4-3 

2-9 

T6 

1.03 

0.62 

830 

<4 

44 

0.58 

0.41 

550 

44 

44 

1 

0.91 

0.55 

730 

44 

44 

0.51 

0.36 

480 

44 

44 

"ft 

0.79 

0.47 

630 

44 

44 

0.45 

0.31 

410 

44 

44 

\ 

0.65 

0.38 

510 

44 

44 

0.37 

0.25 

330 

44 

44 

_ A 

0.51 

0.29 

390 

44 

44 

0.29 

0.20 

270 

44 

• 44 



















































107 


STEEL CONSTRUCTION 

TABLE III (Continued) 
Strength of Beams 


I-Beams; H-Sections; Channels; Angles; and Tees 


SECTION 

Mom¬ 
ent of 
Inertia 

I 

Section 

Modu¬ 

lus 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16,000 
Lb ,per 
Sq. In. 

Extreme 
Length for 
Deflection for 
Plastered 
Ceilings 
Limit 1-480 
Span 

SECTION 

1 

Mom¬ 
ent for 
Inertia 

I 

Section 

Modu¬ 

lus 

_I_ 

c 

Resisting 
Moment 
Based on 
Unit 
Stress 
of 16.000 
Lb. per 
Sq. In. 

Extreme 
Length for 
Deflection for 
Plastered 
Ceilings 
Limit 1—480 
Span 

For 

Uni¬ 

formly 

Distrib¬ 

uted 

Load 

For 

Cen¬ 

ter 

Load 

For 

Uni¬ 

formly 

Distrib¬ 

uted 

Load 

For 

Cen¬ 

ter 

Load 

. 

Flange X Stem 

X Weight 

(In.) 4 

(In.) 3 

Foot¬ 

pounds 

Ft. In. 

Ft. 

In. 

Flange X Stem 

X Weight 

(In .) 4 

(In .) 3 

Foot¬ 

pounds 

Ft. In. 

Ft. 

In. 

T-5 x3 -13.6 

2.6 

1.18 

1,570 

6-9 

4-6 

T-3 x3 -10.1 
9.0 
7.9 
6.8 

2.3 

2.1 

1.8 

1.6 

1.10 

1.01 

0.86 

0.74 

1,470 

1,350 

1,150 

990 

6-3 

44 

44 

44 

4-3 

44 

44 

44 

T-5 x2*-n b 

1.6 

0.86 

1,150 

5-6 

3-8 

T-4-Jx3Ul5.9 

5.1 

2.13 

2,840 

7-2 

4-9 

T-3 x2j- 7.2 
6.2 

1.1 

0.94 

0.60 

0.52 

800 

690 

5-4 

44 

3-6 

44 

T-4|x3 - 8.6 
-10.0 

1.8 

2.1 

0.81 

0.94 

1,080 

1,250 

6-9 

44 

4-6 

a 

T-2|x2 - 7.4 

1.1 

0.75 

1,000 

4-6 

3-0 

T-4ix2|- 8.0 
9.3 

1.1 

1.2 

0.56 

0.65 

750 

870 

5-9 

44 

3-10 

it 

T -2^x3 - 7.2 
6.2 

-1.8 

1.6 

0.87 

0.76 

1,160 

1,010 

6-0 

<4 

4-0 

44 

T-4 x5 -15.7 
12.3 

10.7 

8.5 

3.10 

2.43 

4,140 

3,240 

10-6 

44 

7-0 

a 

T-2|x2U 6.8 
5.9 

1.4 

1.2 

0.73 

0.60 

970 

800 

5-8 

44 

3-9 

44 

T-4 x4*-14.8 
11.6 

8.0 

6.3 

.2.55 

1.98 

3,400 

2,640 

9-6 

44 

6-3 

it 

T-2^x2j- 6.5 
5.6 

1.0 

0.87 

0.59 

0.50, 

790 

670 

3-6 

44 

5-3 

44 

T-4 x4 -13.9 
10.9 

5.7 

4.7 

2.02 

1.64 

2,690 

2,190 

8—6 

5-8 

<4 

T-2^xU- 3.0 

0.094 

0.09 

120 

3-0 

2-0 

T-4 x3 - 9.3 

2.0 

0.88 

1,170 

6-8 

4-6 

T - 2 jx 2 j - 5.0 
4.2 

0.66 

0.51 

0.42 

0.32 

560 

430 

4-9 

44 

3-0 

44 

T-4 x2j- 8.7 
7.4 

1.2 

1.0 

0.62 

0.55 

830 

730 

5-8 

44 

3-9 

44 

T-2 x2 - 4.4 
3.7 

0.45 

0.36 

0.33 

0.25 

440 

330 

4-0 

44 

2-9 

44 

T-4 x2 - 7.9 
6.7 

0.6 

0.54 

0.40 

0.34 

530 

450 

4-r6 

44 

3-0 

44 . 

T-2 xlj- 3.2 

0.16 

0.15 

200 

3-3 

2-2 

T-3jx4 -12.8 
10.0 

5.5 

4.3 

1.98 

1.55 

2,640 

2,070 

8-4 

44 

5-6 

4 4 

T-l?xlf- 3.2 

0.23 

0.19 

250 

3-8 

2-6 

T-l|xlU 2.6 
2.0 

0.15 

0.11 

0.14 

0.11 

190 

150 

3-3 

44 

2-2 

44 

T-3^x3U11-9 

9.3 

3.7 

3.0 

1.52 

1.19 

2,030 

1,590 

7-6 

44 

5-0 

44 

T-lixlU 2.1 
1.7 

008 

0.06 

0.10 

0.07 

130 

93 

2-6 

44 

1-9 

44 

T-3jx3 -11.0 

8.7 

7.7 

2.4 

1.9 

1.6 

1.13 

0.88 

0.72 

1,510 

1,170 

960 

6-6 

44 

44 

4-4 

44 

44 

T-l Xl - 1.3 

1.0 

0.03 

0.02 

0.05 

0.03 

67 

40 

2-0 

44 

1-4 

44 

T-3 x4 -11.9 
10.6 
9.3 

5.2 
4.8 

4.3 

1.94 

1.78 

1.57 

2,590 

2,370 

2,100 

8-0 

it 

tl 

5-4 

44 

44 







T-3 x3| 11.0 

9.8 

8.6 

3.5 

3.3 

2.9 

1.49 

1.37 

1.21 

1,990 

1,830 

1.610 

7-2 

a 

a 

4-9 

44 

44 































































10S 


STEEL CONSTRUCTION 


This can be applied to designing girders for floor panels. Fig. 
86 shows a section of floor with several arrangements of joists. 
When the girder length is divided by the joists into an even number 
of spaces as 2, 4, and 6 in (a), (b), and (c), respectively, Fig. 86, the 
bending moment on the girder is the same as if the entire panel load 
were uniformly distributed over the length of the girder. When the 
girder length is divided by the joists into an odd number of spaces 
as 3, 5, and 7 in (d), (e), and (f), respectively, the bending moment 
is less than if the entire panel load were uniformly distributed over 
the length of the girder. 

Problem 

To prove the foregoing statements, assume panels 20 feet square and a 
load of 100 pounds per square foot. Compute the bending moments on the 
girder for all the cases illustrated in Fig. 86. 



Fig. 86. Diagrams of Girders Showing Types of Joist Spacing 


Shearing Resistance. It has been stated, p. 79, that the maxi¬ 
mum shear in a beam section can be determined approximately by 
assuming that the entire shear is resisted by the web of the beam. 
For this purpose the area of the web may be taken as the total depth 
of the beam multiplied by the thickness of the web. Then the total 
resistance V is the area of the web A multiplied by the allowable 
unit shear S s and is expressed by the formula 

FWXS. 

The unit stress allowed is 10,000 pounds per square inch. For 
example, to determine the shearing resistance of a 12" I 40 

A= 12X0.46 =5.52 sq. in. 
then V =5.52 X 10,000 = 55,200 # 

Problem 

Refer to the problems given under bending resistance. Compute the* 
•shearing resistance of the beams and compare with the maximum shearing stress., 









STEEL CONSTRUCTION 


109 


The shearing resistance is usually much in excess of the amount 
required. It need not he investigated unless the span is short or 
unless a heavy load is applied near a support so that it produces a 
small bending moment and high shear. The values of the shearing 
resistance of beams are given in Table III. By the use of this table 
the shearing resistance of the beam which has been selected can be 
compared with the computed maximum shear on the beam. 

Of more importance is the strength of the standard end connec¬ 
tions for beams. These are discussed in a later section of this text. 
Their values are given in Table III. In all cases the strength of the 
connection is less than the shearing strength of the beam. Hence, 
the strength of the connection must be compared with the maximum 
shear on beams. If the standard connection is not strong enough, 
a special one must be devised and the strength of the web investi¬ 
gated. 

Deflection. The deflection of a beam may be of as much 
importance as its strength. If its amount is noticeable, it gives 
the impression of weakness. This is especially true when it shows 
a definite change under the application and removal of live load. 
If the beam deflects unduly, it will cause cracks in the supported 
material. The most common results of too much deflection are 
cracks m plaster under the middle of joist spans and cracks in tile 
or concrete floors over the ends of joists where they connect to 
girders. This is shown in an exaggerated way in Fig. 70. It is not 
uncommon to find such unsightly cracks in the tile or marble floors 
of high-grade buildings. It has been determined experimentally 

that plaster will crack when the deflection is —- of the span, i. e., 

3o0 

1 inch in 30 feet; but a much lower value should be used for masonry 
and for marble floors and ceilings. 

Deflection Formulas. Deflection formulas (p. 80) are as follows: 


for uniformly distributed load 
for load concentrated at center 


d = 


5 IF/ 3 


384 E I 
1 IF/ 3 
48 El 


in which d is deflection in inches; IF is total load; / is length in 
inches; E is modulus of elasticity; and I is moment of inertia. 





110 


STEEL CONSTRUCTION 


To illustrate their use, assume a 12" 131^#, span 15 feet, or 
180 inches, load u. d. 25,000 pounds. The value of / for this beam 
is 215.8. Then 

, 5 25.000y ISOX180X ISO 

384 30,000,000X215 8 

If we change the load from u. d. to concentrated 

1 25,000X180X180X180 

48 X 30,000,000X215,8 

A comparison of the results shows that the deflection is l.G 
times as much for the concentrated load as for the uniformly dis¬ 
tributed load. If both the above loads are applied at the same 
time, the total deflection is the sum of the two amounts computed 
above, i. e., 

d = 0. 29"-f0.47" = 0.7G" 


Formulas are given in the handbooks for other forms of loading, 
but as they are not used often they are not given here. Concentrated 
loads within the middle third may be treated as if at the center, and 
if outside the middle third, as if uniformly distributed. The results 
from this approximate method will be reasonably close to the cor¬ 
rect values. 


Safe Span Length. Based on a maximum deflection of of 


the span, and on a unit stress of 1G,000 pounds per square inph, the 
permissible span is 25 times the depth for a uniformly distributed 
load and IS.6 times the depth for a center load. These relations are 
correct for sections symmetrical about the neutral axis, as I-beams 
and channels. They err on the safe side for unsvmmetrical sections, 
as angles and tees, and may be used for them. These values should 
be considered the extreme lengths for beams loaded to their full 
capacity. It is preferred that shorter lengths be used for several 
reasons: viz, noticeable deflection is objectionable; the greatest 
practicable stiffness is desired; deflection causes secondary stresses 
in the connections. 

The handbooks, in their tables of “Safe Loads Uniformly Dis¬ 
tributed for I-beams”, limit the span length for deflection to 24 
times the depth. The designer must use his judgment in this 
matter, giving consideration to the conditions of loading. A con- 





STEEL CONSTRUCTION 


111 


venient rule for a u. d. load is 2 feet of length for each inch of depth 
(24 times the depth); and for a center load 1 j feet of length for 
each inch of depth (1G times the depth). Table III gives the max¬ 
imum allowable spans for these ratios, based on a unit stress of 
16,000 pounds per square inch. If, however, the unit stress is less 
than 10,000 pounds, longer spans may be used. 

In most cases the beam section required to resist the bending 
moment comes well within the limiting length for deflection. It is 
only when a long span has a relatively light load that deflection 
must be considered. This condition occurs most frequently in joists. 
Girders rarely have excessive deflection. 

To illustrate such a case, assume a beam of 30-foot span sup¬ 
porting a load of 8000 pounds u. d. The bending moment is 30,000 
foot-pounds, which requires 10" I 25 #. The length of this beam is 
3G times its depth, therefore the deflection will be excessive- If it is 


decided arbitrarily to make the depth of beam — of the span, the sec¬ 


tion required is 15" I 42$. This beam, if loaded to full capacity, 
would deflect just to the allowed limit. But the resisting moment 
of 15" I 42# is 79,000 foot-pounds, more than twice the bending 
moment computed above, hence its deflection being in direct pro¬ 
portion to the load is less than half that allowed. Assume that the 

deflection must not exceed 1 inch, i. e., —-of the span. Then try 

3G0 

12" I 3H# and compute the deflection from the formula 


5 IVP _ 5 w 8000X360X360X360 
384 E1 384 X 30,000,000X215.8 


As the computed deflection is less than the allowed amount, the 
12-inch I-beam is satisfactory. 

The problem can be solved directly instead of by trial. Trans¬ 
form the equation to the form 


5 


/ = 3S4 X 


WP 5 w 8000 X 360 X 360 X 360 _ ino 

X _ __^ ^ ^ 1 v) J 


Ed 384 


30,000,000X1 


The beam having a value I next higher than 162 is 12" I 31^ #. The 
handbooks give explanations and tables for aiding the solution of 
this problem. 







112 


STEEL CONSTRUCTION 


Attention is called to the fact that usually a joist receives a 
considerable percentage of its load (the floor construction) before 
the plastering is done. It has already deflected in proportion to the 
load it has received. It is only the subsequent loading and the 
resulting deflection that may crack the plaster. Consequently, the 


total deflection might be much greater than 


1 

360 


times the span and 


still not cause trouble. Nevertheless it is best to keep within this 
limit. 

. The situation regarding marble or concrete floors is quite 
different. Fig. 70 illustrates in an exaggerated way the joists in 
two panels, connecting to a cross girder. It takes but little deflection 
to cause cracks in the floor over the girder. No definite limit of 
deflection has been determined for this case. The writer has ob¬ 
served an instance where the deflection appeared to be less than 


3 

8 


inch in a span of 24 feet (about 



No definite suggestion can 


be made for taking care of this difficulty other than to make the 
joists as stiff as practicable within a reasonable cost. Probably this 
trouble can best be eliminated by the use of elastic joints in the 
floor over the girder. 

Problem 

What I-beam is required to support a u. d. load of 4500 pounds on a span 
of 24 feet the permissible deflection being Yi inch? 


Lateral Support. If the top flange of a beam is not supported 
laterally, it is in much the same condition as a column. It is then 
not capable of supporting the full load given by the beam formula. 
In many cases where the lateral support is not furnished by the floor 
construction, connecting beams, or otherwise, it can be supplied by 
means of tie rods or struts inserted for that purpose. When no 
such lateral support can be provided, the allowable load must be 
reduced. 

The handbooks contain tables which give the proportion of the 
total load that may be used for various ratios of length to width of 
flange. They permit the full load when the unsupported length is 
less than 20 times the width. 

To illustrate the use of these tables assume a 12" I 31^# 20 feet 
long, supported laterally at the center. The unsupported length is 




STEEL CONSTRUCTION 


113 


10 feet, or 120 inches. ( The width of flange is 5 inches. Then the 

ratio of length to width of flange is —— = 24. In the Cambria 

5 

handbook, the allowable load is 94 per cent of that given by the 
beam formula. 

In Table III, the extreme' lengths are given for beams without 
lateral support when loaded to full capacity and when loaded to 
half capacity. Intermediate values can be interpolated. The 
lengths given are, respectively, 20 and 60 times the flange width. 
In all cases beams must have lateral support at the end bearings. 
Problems 

1. What is the safe resisting moment of an 8" X 18# on a 12-foot span when 
the top flange has no lateral support? 

2. The required resisting moment of .a beam is 42,000 foot-pounds; its 
unsupported length is 12 feet. What I-beam is required? 

PRACTICAL APPLICATIONS 

Panel of Floor Framing. Fig. 87 illustrates a typical floor 
panel in a building. It is desired to investigate the various possible 
arrangements of framing for this panel. Assume that the dead 
load on the joists is 80 pounds per square foot including the weight 
of joists (but not the weight of the girders and their fireproofing); 
assume that the live load is 100 pounds per square foot on-joists, 
and 85 pounds per square foot on girders. 

Scheme (a). Scheme (a) places the girders on the longer span 
and divides the panel into 4 parts. The joists are spaced 5'-4|" c. c. 

Area supported by one joist 16 X 5| = 86 sq. ft. 

dead load on one joist 86 X 80 = 6880# 
live load on one joist 86X100 = 8600# 

Total load 15,480# 

This total load, 15,480 pounds, is uniformly distributed on a span 
16 feet. The table of safe loads in the handbook indicates 10" 

I 25#. 

The girder carries the reaction of the joists on each side and the 
weight of itself and of its fireproofing (assumed at 200 pounds per 
lineal foot). On the theory that the whole floor will not be loaded 
at one time, the live load on the girder is taken at 85 pounds per 




. 1 ,« 

X 65 * 





. / 

u„. 


l, 

* 

V) 

-5'sf- 

1 

o> 

< 

*Nj>— 

_ 

-5-4'- 




* 

> 



, 


<Vj 





c 


"i 





§ 

DO. 

Q> 

Ci 

DO 

DO. 

\ 


V? 

•v 

DO 


<s 

c» 

















DO. 


' 




DO. 




— 

, 


r 'i 

- ^ 

, 



1 1 

1 1 1 


(O 



1 


(d) 





) 




\ 





J 

T 



> 


1 



1 


i 



1 1 








i 

i 


(f) 

-H-—-M 


D L 86 X.SO*68BO 
L L 66X85-75/0 



/S/so 

/S/so 

/4/90 


—5'-4jr~ 





^—* 


l '•!■!, r 

^0f A 800 - 4100 

r TT~l 


X 


- 80 - 6 - 


X 


2//5S 
8050 
25/8 5 


8/US 
80S O 

25/85 


Fig. 87. A Panel of Floor Framing 






























































STEEL CONSTRUCTION 


115 


square foot. The length of span is taken at 20'-6" (allowance being 
made for the width of the column). Then the loads~on the girder 
are as indicated in the figure and the bending moments are 


for u. d. load 


4100X20^ 

8 


= 10,500 ft.-lb. 


for concentrated loads 


f +21,135X101 = 216,634 
14,190 X 5§ =-76,271 

-= 140,363 


Total bending moment = 150,863 ft.-lb. 


From the table of resisting moments, p. 100, 20" I 65# is indicated. 

Scheme ( b ). Scheme (b) places the girders on the longer span 
and divides the panel into 3 parts. This requires for the joists 
12" I 31^#; and for the girders 20" I 65#. 


EXAMPLES FOR PRACTICE 


(c). 


1. Determine the sizes of joists and girders required for scheme 


2. Determine the sizes of joists and girders required for scheme 
(d). Note that the girders are to be made of two I-beams. This 
makes the span of the joists 15'-4". 

3. In scheme (e) the girder is placed on the shorter span, as 
shown. Its net length is 15'-0". Determine the sizes of joists and 
girders. 

4. Determine the sizes of I-beams required for scheme (1;. 

5. In scheme (g) it is desired to make the joists and girders 
the same depth. This makes it necessary to use two I-beams for the 
girder. What sections are required? 

6. Investigate all the beams in the foregoing problems as to 
shear, deflection, and strength of standard end connections. 

7. Compute the weight of the I-beams required for one panel 
for each of the above schemes. There is one girder for each panel, 
and one joist for each division of the panel, i. e., four joists for 
scheme (a), three for scheme (b), etc. The weights for scheme (a) are 


4 10" I 25 # X15'-l 1" = 1592 # 

1 20" I 65#X20'- 6" = 1333# 

8. Which scheme requires the least weight of steel? 





11G 


STEEL CONSTRUCTION 


Choice of Scheme. A number of considerations will affect the 
final decision as to the scheme to be adopted. The character of 
the floor construction will limit the spacing of the joists. It might 
eliminate schemes (b), (c), (d), and (f). The thickness of floor 
construction may be important, in which case scheme (a) would be 
preferred as to joists and scheme (g) as to girders. The thickness 
of floor may affect it?s cost and also the dead load to be carried by 
joists, girders, and columns, making the thinner floor preferable on 
this account. A flat ceiling may be required over the entire area, 
in which case scheme (g) is applicable. 

Problem 

A space 14 feet wide and 100 feet long is to be floored over. This floor is 
to be supported by joists resting on brick side walls. The floor construction is 
such that the joists may be spaced not more than 8 feet c. c. Total load 200 
pounds per square foot. Determine the most economical size and spacing of 
joists. 

Lintels. Flat-topped openings through brick walls require 
lintels to support the masonry above. Brickwork, after it has 
hardened, will arch over such openings, the part of the brickwork 
below the thrust line of the arch being held in place by adhesion of 
the mortar. But there must be some support while the mortar is 
green, or the arch action may be destroyed by settlement, making 
a permanent support necessary. The amount of the load on lintels 
is uncertain. Each case must be decided according to the condi¬ 
tions. , 

Types of Construction. In Fig. 88 several cases are illus¬ 
trated. 

Case a is an opening with a solid wall above and at the sides. 
A satisfactory rule in this case is to figure the weight of brickwork 
within the triangle whose base equals the width of opening and whose 
slopes are 45 degrees. 

In case h the shaded area might be entirely supported on the 
lintel over the lower opening. 

Case c represents a spandrel wall between piers. The height of 
the brickwork is less than the width of the opening. The entire 
weight of the spandrel should be supported on the lintel. 

In addition to the weight of the brickwork, the lintel may have 
to support the end of a girder as in case d, or it may have to support 
some floor area as in case e. 


STEEL CONSTRUCTION 


117 


Case/ shows a section through a wall in which the outer course 
ol brickwork is supported by a lintel and the remainder by an arch. 

In the following problems assume the weight of brickwork to 
be 120 pounds per cubic foot. Then for each superficial foot of wall 
the weight is 10 pounds for each inch of thickness. 



EXAMPLES FOR PRACTICE 

1. Design lintel for case a, span 4 feet, wall thickness 9 inches. 
Use 2 Ls. The horizontal legs of the angles should be 3| or 4 inches 
wide to support the brickwork properly. See Table II for formula 
for bending moment for this condition of loading. 

2. Design the lintel required for conditions given for case b. 
Assume that the channels carry the entire load. 








































































118 


STEEL CONSTRUCTION 


3. What section of I-beam is required for the lintel in casec? 
Neglect the value of the plate on the bottom of the beam. 

4. In case d assume a load of 20,000 pounds from the girder in 
addition to the weight of brickwork. What section of I-beam and 
channel are required? Neglect the value of the angle. 

5. In case e assume a load of 2000 pounds per lineal foot in 
addition to the weight of the wall. What section of I-beam and 
channel are required? The span is the same as for case c. 

6. Determine the angle required to support the face brick 
across a 5-foot opening. (Case /). (The back is supported by 
brick arches.) 

Cantilevers. Fig. 89 shows a beam projecting beyond the wall 
of a building, that is, a cantilever beam. The projection is 6 feet 


• t 

fp 

1 

1 1 

Ay/" 

1 



Fig. 89. Cantilever Construction 


from the face of the wall. The load to be suspended from the end 
of the cantilever is 10,000 pounds. Within the building the beam 
serves as a girder on a span of 16 feet. As such it supports a dead 
load of 1600 pounds per lineal foot and a live load of 1700 pounds 
per lineal foot. 

Problem 

Compute, from the data given above, the reactions and construct the 
moment and shear diagrams for each of the three following combinations of 
loading and determine the I-beam required: 

i 

(1) Dead load and live load 

(2) Dead load and suspended load 

(3) Dead load, live load, and suspended load 

Tank Support. Fig. 90 illustrates the framework for supporting 
a wood water tank. The tank rests on 4"X6" wood sub-joists 





















STEEL CONSTRUCTION 


119 


spaced about 18 inches center to center. These in turn rest on 
steel joists. The load on the steel joists may be considered as 
uniformly distributed. 



— /e-o- -——► 


1 ' 






1 1 1 1 1 i 




- 

it 



To compute the volume and weight, use the outside dimensions 
of the tank. (Assume the weight of water to be 62.5 pounds per 
cubic foot.) This will give some excess which will be sufficient to 
cover the weight of the steel beams. On this basis 

volume = 3,1416 * 1 -- X - 13 X16=2125 cu. ft. 

4 

weight =2125X62.5 = 132,800# 




















































120 


STEEL CONSTRUCTION 


This can be used as a check on the sum of the partial loads. The 
load per square foot for 16 feet of water is 16X62.5 or 1000 
pounds. 

Problems 

1. Lay out an assumed plan of the framework and the outline of the tank 
accurately to scale. Determine the area supported by each beam by measure¬ 
ments from the scale drawings as indicated by the shaded areas in the figure. 

2. Compute the bending moment and shear for the several joists and the 
girders, and select the required I-beams. Check for strength of end connections. 


DETAILS OF CONSTRUCTION 

Connection of Beams to Beams. When one beam bears on top 
of another, the only connection required is rivets or bolts through 
the flange, as shown in Fig. 91. No stress is transmitted by these 



Fig. 91. Riveted Con¬ 
nection of Beam to 
Beam 



Fig. 92. Beam Connections by Means of Sheet 
Steel Clips 


rivets or bolts. They serve simply to hold the beams in position. 
Steel clips are sometimes used for this purpose, Fig. 92, but as they 
are not positive in holding the beams in position they are not as 
good, especially when lateral support is required. When this is not 
important, the clips can be used and may effect a saving in cost. 
These clips are most useful for attaching tees and angles to beams in 
ceiling and roof construction. 

Angle Connections. Fhe most common method of connecting 
one beam to another is by means of angles riveted to the web. There 
are several sets of standard connections, various concerns having 
their own standards, hose of the American Bridge Company are 



























STEEL CONSTRUCTION 


121 


given in Fig. 93.* The values given in Table III are based 
on these. The two-angle connection is generally used, but when 
beams are used in pairs or *when for any reason the two-angle con- 



Used by American Bridge Company 

nection cannot be used, the one-angle connection is used. The 
rivets used in the standard connections are | inch in diameter. 

♦Subsequently a different set of standards has been adopted. See Carnegie Pocket Com¬ 
panion, 1913 edition. 




























































































































































































































122 


STEEL CONSTRUCTION 


The strength of the two-angle connection may be limited by 

(1) Shop rivets in double shear 

(2) Field rivets in single shear 

(3) Shop rivets in bearing in web of joist 

(4) Field rivets in bearing in web of girder 

For example, take the connection for a 15" I 42$: 

(1) 6 shop rivets in double shear 


6X10,300 =61,800# 

(2) 8 field rivets in single shear 


8X 4420 =35,360# 

(3) 6 shop rivets in bearing in web of joist 

6 X . 41X . 75 X 25,000 = 46,125 # 

(4) 8 field rivets in web of girder; the thickness of the web is not 
given. It must be at least 0.30 inch for a connection on one 
side only, or of twice this thickness if an equal connectioh 
is on the opposite side, in 
order to have the same 
strength as the field rivets 
in shear. 


i?"I Jl 


,# 


COPE TO 
!d"l 55* 


e 



Fig. 94. Plate Riveted to Web of 
I-Beam to give Additional 
Bearing 



COPE TO . 
!Z"1 3 // 


Fig. 95. Diagrams of Coped Beams 


The shearing strength of this connection, 35,360 pounds, corre¬ 
sponds to the maximum safe u. d. load on a span of about 9 feet. 
It is less than the shearing strength of the web of the beam. It 
rarely happens that the strength of the connection is less than 
required, and occurs only when the beam is short and heavily loaded 
or when a heavy load is applied near the end. Lack of bearing in 
the web of the girder is more likely to occur, but this is not fre* 












































































































































































































124 


STEEL CONSTRUCTION 


quent. If it does happen, however, angles with 6-inch legs may be 
used to provide space for more rivets, or a reinforcing plate may 
be riveted to the web of the girder, Fig. 94. 

Special Connections. When beams on the two sides of a girder 
do not come opposite or are of different sizes so that the standard 
connections do not match, it is necessary to devise a special connec¬ 
tion. If a beam is flush on the top or on the bottom with the one to 
which it connects, the flange must be coped, Fig. 95. A number of 
special connections are shown in Fig. 96 and need no explanation. 

Connections of Beams to Columns. A beam may connect to a 
column by means of a seat or by means of angles on the web. The 

great variety of conditions that 
may be encountered make it im¬ 
practicable to have standards for 
these connections, though the 
work of each shop is standard¬ 
ized to some extent. 

Seat Connections. The seat 
connection is shown in Fig. 97. 
This seat or bracket is made up 
of a shelf angle, one or two 
stiffener angles, and a filler plate. 
The load is transmitted by the 
rivets, acting in single shear, 
which connect the bracket to the 

Fig. 97. Seated Connection of Beam to CotUmn . 

column, lhe number of rivets 
used is proportioned to the actual load instead of being standardized 
for the size of the beam. The stiffener angles support the horizontal 
leg of the shelf angle and carry the load to the lower rivets of the 
connection. 

Shelf angles are 6 inches, 7 inches, or 8 inches vertical and 4 
inches or 6 inches horizontal, having a thickness of & inch to f inch, 
depending on the size of beam and the load. The leg of the stiffener 
angle parallel to the w r eb of the beam is usually \ inch or 1 inch less 
than the horizontal leg of the shelf. The leg against the column is 
governed by the gage line of the rivets in the column. The filler is 
the same thickness as the shelf angle. An angle connecting the top 
flange of the beam to the column is generally used. It is not counted 


































STEEL CONSTRUCTION 


125 


as carrying any of the load, but serves to hold the top of the beam 
in position and stiffens the connection. The rivets connecting the 
bottom flange of the beam to the shelf serve only to hold the mem- 



Fig. 98. Types of Seat Connections 


bers together and make a stiff connection. Usually there are only 
two rivets in each flange but sometimes larger angles and more 

























































































































126 


STEEL CONSTRUCTION 


rivets are used to develop resistance to wind stresses. Fig. 98 gives 
a number of examples of seat connections. 

The advantages of the seat connection are 

(1) All shop riveting is on the column which is a riveted 
member. No shop riveting is required on the beam 
which thus needs only to be punched 

(2) The seat is a convenience in erecting 

(3) The rivets which carry shear are shop driven 

(4) The number of field rivets is small 

Web Connections. The web connection is made by means of 
two angles, Fig. 99. The legs parallel to the beam rivet to the 

web and the outstanding legs to 
the columns. The connection to 
the web of the beam is governed 
by the same conditions as the 
standard beam connection. The 
length of the outstanding leg is 
governed by the gage lines of the 
rivets in the column or the space 
available for them. Usually the 
angles are shop riveted to the 
beam and field riveted to the 
column. If the angles were shop riveted to the column, it would be 
difficult or impossible to erect the beam. However, one angle may 
be shop riveted to the column and the other furnished loose. In this 
case the number of field rivets generally will be the same as if the 


-i- 


r 



Fig. 99. Web Connection of Beam to Column 



Fig. 100. Diagrams Showing Disadvantage of Seat Connection for Fireproofing 


angles were shop riveted to the beam, but the shop riveting on the 
beam will be eliminated, which is an advantage. When this connec- 




































































STEEL CONSTRUCTION 


127 


tion is used, a small seat angle is provided for convenience in 
erecting. ^ 

The advantage of the web connection is the compactness of 
the parts, keeping within the limits of the fireproofing and plaster, 
whereas the seat connection may necessitate special architectural 
treatment to fireproof it or conceal it, Fig. 100. 

Combination Connections. A combination of web and seat 
connections may be used to meet special conditions. For example, 
the load may be too great for a web connection, and at the same 
time a seat connection may be objectionable. The combination 
will reduce the seat connection to a minimum, perhaps eliminating 
the stiffener angles. Another case is where top and bottom angles 
are required for wind bracing but stiffener angles are not permitted; 
there the combination can be used. 

The objection to the combination is that there are two groups 
of rivets for supporting the load. If the connection is not accurately 
made, the entire load may be carried by one group of rivets. A 
number of miscellaneous connections are illustrated later in the text 
under column details. 

Separators. When beams are used in pairs or groups, some 
connection is usually made between them at short intervals. The 
connecting piece is called a "sep¬ 
arator”. If the purpose to be 
served is merely to tie the beams 
together and keep them properly 
spaced, the gas-pipe separator is 
used, Fig. 101. This consists of 
a piece of gas pipe with a bolt 
running through it. This form 
is used in lintels and in grillage 
beams. For beams 6 inches or less in depth, one separator and 
bolt may be used; for greater depth, two should be used. 

The separator most commonly used is made of cast iron, Fig. 
1(J2. It not only serves as .a spacer but it stiffens the webs of the 
beams and, to a limited extent, transmits the load from one beam 
to the other in case one is loaded more heavily. It seldom fits 
exactly to the beam so it cannot be relied upon to transmit much 
load. One bolt is used for beams less than 12 inches deep and two 



f ••• * 


Fig. 101. Gas-Pipe Separators 

















128 


STEEL CONSTRUCTION 


bolts for 12-inch and deeper beams. The dimensions and weights 
of separators and the bolts for them are given in the handbooks. 
They can be made for any spacing of beams and special shapes can 



Fig. 102. Cast-Iron Separators 



be made for beams of different sizes. 
Fig. 103. 

The individual beams of a pair 
or group should be designed for the 
actual loads which they carry, if it is 
practicable to do so. If it is necessary 
to transfer some load from one to the 
other, a steel separator or diaphragm 
should be used. This may be made of a 


/ 



Fig. 104. Steel 



plate and four angles or of a short piece of I-beam or channel, Fig. 
104. If the beams are set close together, the holes must be reamed 
and turned bolts must be used in order to get an efficient con- 























































STEEL CONSTRUCTION 


129 


•nection. If the beams are set with four inches or more clearance 
between the flanges, the separator can be riveted to the beams. 

Specifications usually require that separators be spaced not 
further than five feet apart. They should be placed at points of 
concentrated loads and over bearings. 


GIRDER 




• 


$ 

o 

: 

' 







GIRDER 




Fig. 105. Layout Showing Tie-Rod Connections Between Joists 


Tie=Rods. A common form of fireproof floor 4 construction is 
the hollow tile arch between steel joists spaced from 5 feet to 7 feet 
apart. The arch exerts a thrust sidewise on the beams and would 
spread the beams apart and cause the arch to fall, if they were not 
tied together. Rods f inch in diameter are used for these ties. 
They are spaced about 6 feet apart and placed 3 or 4 inches above 
the bottom of the beams. After the arch construction is in place, 
the thrusts on the two sides of a beam would balance if equally 



5ECMERTAL TERRA COTTA ARCH COHSTRUCDOh 
Fig. 106. Tie-Rod Connections for Segmental Arches 


loaded so that under these conditions the rods would be needed 
only in the outside panels. However, they are needed in all panels 






































130 


STEEL CONSTRUCTION 


during construction and as the loads on the several panels may be 
unequal, they are retained throughout the floor construction, Fig. 105. 

If long span segmental arches are used, the thrust is much 
greater. Its amount must be computed and the tie-rods propor¬ 
tioned for the actual stress, Fig. 10G. 

Bearings. Dimensions of Bearing Plates. Under Unit 
Stresses are given the safe bearing values on masonry. The end of 
a beam resting on masonry' usually does not have sufficient bearing 
area, and a bearing plate is required. The area of the plate is 
determined by dividing the load (the end reaction of the beam) by 
the allowed unit pressure on the masonry. For example, assume a 

15" I 42# bearing on a wall of hard brick in 
cement mortar, the reaction at the bearing being 
18,000 pounds. The allowable pressure is 200 
pounds per square inch. Then the required 

area of the plate is or 90 square inches.. 




— 12- --1 


-3p- 


-34- 

r 

<*> 


I i 

1 1 

1! 

II 


1 


11 

u_. 



i! 

1 1 



A plate S"X 12" or one 1.0" X10" would be used. 

The required thickness of the bearing plate 
depends on the pressure per square inch on the 
masonry and the projection of the plate beyond 
the flange of the beam. This projecting portion 
of the plate acts as an inverted cantilever with a 
u. d. load. Thus in Fig. 107 the beam is a 15" 
I 42#, the plate 8"X 12". The projection of the 
plate is inches and the upward pressure per 
square inch is 200 pounds. To determine the 
thickness, assume a strip 1 inch wide; then there 
is a cantilever 3} inches long with a load of 200 pounds per inch. 
The bending moment is 

3.25X200X— Q —= 1050 in.-lb. 






|g 


Fig. 107. Diagram Show¬ 
ing Bearing Plate.. 


From the bending moment the required section modulus - can be 

c 

obtained by the formula given on p.-98; and from it the thickness t 
of the plate can be obtained by the formula given on p.-37, thus 

I M 1050 


c 8 10,000 


- .000 


















STEEL CONSTRUCTION 


131 


From the section modulus the thickness t can be computed by 
the reverse of the method previously given for computing I, thus 


7 = 6 = 1" c = 

1 = 

c 12 t_ 6 
2 


t 

2 


< 2 =6X-=6X .066= .396 

c 


<=V.396 = 0.63", or f" thick 

The square root can be figured by the usual rules but can be 
obtained more easily from tables in the handbook. 

Graphical Diagram for Designing Bearing Plates. Fig. 108 is a 
graphical diagram for designing bearing plates. Along the left side 



Fig. 108. Diagram for Determining Thickness of Steel Bearing Plates' 

is given the projection of the plate in inches; along the bottom is 
the thickness in inches; the diagonal lines represent the several 
allowable pressures for different classes of masonry. Having com¬ 
puted the size of plate needed for bearing, find the amount of its 
projection beyond the flange of the beam. Enter the diagram at 
the left on the horizontal line corresponding to the projection; trace 

































































132 


STEEL CONSTRUCTION 


<€ p ] p 


I 


Lt: r._ 


it# 

Mt 




Hi 


ir 1 


to the right to the diagonal line representing the pressure; then 
vertically downward to the bottom of the diagram and read the 
thickness. For example, assume a projection of 3| inches and an 
allowable bearing of 200 pounds per square inch; the required thick¬ 
ness is f inch. 

Standard Bearing Plates. In the handbooks are given standard 

> 

bearing plates for the various sizes of beams. One size of plate is 

given for each size of beam, hence 
these standard plates are designed 
for the heaviest loads likely to 
be carried by the heaviest beam 
section and, consequently, are 
larger than needed for most cases. 
In the example given above, the 
Cambria standard plate is 12" X 
15" Xf". It is larger than re¬ 
quired, thus showing that it is 
economical to design the plates 
for the actual loads and the 
allowable bearing pressures. In 
this same example, if the bearing 
is on concrete at 400 pounds per 
square inch, no plate is required 
as the beam flange alone gives 
the necessary area. 

Penetration into Wall. The 
penetration of beams into the 
wall, if the thickness of wall 
permits, should be not less than 

Fig. 109. I-Beams Used For Bearing the following *. 

for 3-inch, 4-inch, 5-inch, and 6-inch beams and channels 6 inches 

for 7-inch, and 8-inch beams and channels 8 inches 

for 9-inch, and 10-inch beams and channels 10 inches 

for 12-inch, and 15-inch beams and channels 12 inches 

for 18-inch, 20-inch, 21-inch, and 24-inch beams and channels 15 inches 

When the thickness of the wall does not permit the penetration 
recommended above, the allowable bearing stress should be reduced. 
The reduction should be 50 per cent for heavy beams on an 8-inch 



n 

b 

i 



i 

> 

j 






















































STEEL CONSTRUCTION 


133 


bearing. A penetration less than 8 inches should never be used for 
beams 8 inches or more in. depth. Because all beams deflect under 
load their bearing plates should be set with a slight slope downward 
toward the face of the wall, | inch per foot being a satisfactory slope. 
This prevents the whole load from being concentrated on the front 
edge of the plate. 

Plates thicker than 1 inch are difficult to get. When this 
thickness is not enough for the projection desired, one or more 




I-beams or channels should be used for the bearing, Fig. 109. These 
are designed as inverted cantilevers in the regular way. 

Cast-Iron Plates. The foregoing discussion relates to steel 
plates. Cast-iron plates may be used. The method of designing 
them is the same as for steel plates, except that the allowable fiber 
stress is 3000 pounds per square inch. On account of this differ¬ 
ence in.the allowable stress, the thickness of the cast-iron plate is 
2\ times the thickness of the steel plate. The diagram, Fig. 108, 
may be used for cast iron by first determining the thickness for 


























































































































134 


STEEL CONSTRUCTION 


steel and multiplying the result by 2\. In most localities the cast 
iron costs more than steel on account of the additional weight. 

Anchors. Beams bearing on masonry are usually anchored to 
it to give greater stability to the structure as a whole. Fig. 110 
shows the common forms of anchors used for this purpose. The 
bent rod a is the cheapest. The angle lugs b are the most efficient. 
The other forms are used for the special conditions indicated. The 
thickness of metal used is arbitrary, usually f inch for rods and 
§ inch for angles and plates. 

Miscellaneous Details. Almost every structure presents some 
conditions requiring special details of the beams. The relative 
position of the steel members may require a special form of con¬ 
nection, or the other materials of construction may necessitate 
special details for their support. A number of such details will be 
shown in connection with the practical designs later in this text. 

RIVETED GIRDERS 


Definition. The term “riveted girder” is here used to apply 
to all riveted beams, i. e., beams made of two or more steel sections 





Fig. 111. Types of Riveted Girders 


riveted together. The most common forms of riveted girders are 
illustrated in Fig. Ill as follows: 

(a) I-beam with flange plates 

(b) Plate girder 


(c) Plate box girder 

(d) Beam box girder 










































STEEL CONSTRUCTION 135 

THEORY OF DESIGN 

Determination of Resisting Moment. All that was stated under 
Review of Theory of Beam Design applies as well to riveted 
girders as to rolled beams, provided the sections are so riveted 
together that they act as a single piece. However, there are two 
methods of determining the resisting moment, viz, by moment of 
inertia and by chord stress, Fig. 112. 

Moment of Inertia Method. The procedure for determining 
the resisting moment of a beam, or girder, by means of the moment 
of inertia has been fully explained. The value of I for the single 




— , ■■ —- - ■ —. 


c 

F=-- 


k 1 

(*) 


3 

t - H 


=■=* 

rf t 


Fig. 112. Diagram of Bending Stresses in a Riveted Girder, (a) Moment of Inertia Method; 

-(b) Chord Method 

rolled section, such as the I-beam, is taken from the tables in the 
handbook, but for the riveted girder it must be computed. 

Chord Stress Method. The second method of designing riveted 
girders assumes that the tensile stresses are resisted by the tension 
flange and the compressive stresses by the compression flange. It 
is assumed that the stress is uniformly distributed over the entire area 
of the flange. Then the moment of resistance is the same as if the 
whole stress were acting at the center of gravity of the flange area. 

The resisting moment determined from the moment of inertia is 

M = S- • 

c 

The resisting moment by the chord method is as follows: In Fig. 
112, t and c represent, respectively, the total tension and total 
compression values of the flanges, applied at the centers of gravity 
of the flange sections. The distance d between them is called the 
“effective depth of the girder”. In order to have equilibrium, t must 
equal c. Each must equal the area A of the flange multiplied by 












































136 


STEEL CONSTRUCTION 


the unit stress S. Then t = c = AxS, and the resisting moment is 

M = AxSxd 

Having determined the bending moment in inch-pounds from the 
loads on a girder, the procedure by the chord method is as follows: 

Assume the total depth of girder and from this approximate the 
effective depth d in inches. This can be taken at 2 to 4 inches less 
than the total depth, depending on the size of flange angles. By 
dividing the bending moment M by the effective depth d, the flange 
stress t or c is obtained; and dividing the flange stress by the 
average unit stress, say 14,500 pounds per square inch, the result is 
the net area in square inches required for the flange. The sections 
required to make up thi§ net area can then be determined. 

The foregoing computations are expressed by the formula 



The average value of the unit stress to be used is proportioned from 
the extreme fiber stress, 16,000 pounds per square inch. Thus if 
the effective depth is T V of the extreme depth, the average unit 
stress to be used is T V of 16,000, or 14,400 pounds per square inch. 

The result of the first trial is only approximate. From the 
section thus determined the value of d can be computed and the 
above operations repeated. This result, which is also approximate 
if any change is made in the section, is usually accurate enough to 
be accepted as final. Most specifications permit | of the web to 
be counted in each flange section. 

Illustrative Example. Assume M equals 420,000 foot-pounds; 
total depth of girder 36 inches; approximate value of d equals 33 
inches. To find the required section 


A = < 


M = 420,000 X12 = 5,040,000 in.-lb. 

A = 14,500X33 = 10 ' 53 
web 36" X A" = 1.41 sq. in. 

2Ls 6"X3FXf" = 11.10 
less 1 rivet hole = 1.10 =10.00 


-4 = 11.41 sq. In. 

As the area of the chosen section is greater than the calculated 
value, it is satisfactory. 





STEEL CONSTRUCTION 


137 


Problem 

Fig. 113 illustrates the plate girder described in the above example. Com¬ 
pute the correct value of d. (Note: No. account is taken of the part of web 
plate which is counted as flange section, in computing the position of the c. g. 
of the flange. Also no account is taken of the rivet 
holes in the web.) Compute the net flange area re¬ 
quired and, if necessary, correct the size of angles. 

The two methods of designing lead to 
about the same results. No further consid¬ 
eration will be given to the chord method, 
as the moment of inertia method is preferred. 

Calculation of Load Effects. The bend¬ 
ing moments and shears are computed in 
just the same manner for girders as for 
beams. However, in making a complete 
design of a riveted girder the bending moment 
is required for all points along the girder 
for computing rivet spacing and fbr deter¬ 
mining the length of cover plates, if they are 
used. Consequently the moment diagram is - 1 — 

needed in most cases. (It can be constructed Fig. 113. Section and Details 
, ,, .ii- '. ,, ,. of Plate Girder 

by the methods given in the sections on 
Bending Moments and Moment Diagrams in “Strength of Mate¬ 
rials”.) 

DESIGN OF PLATE GIRDER 

Having computed the bending moments and shears and con¬ 
structed the diagrams for them, the steps in the design are: 



Determine allowable depth 
Compute thickness of web 
Compute required moment of inertia 
Compute flange section which will give required mo¬ 
ment of inertia 

Determine length of flange plates 
Design stiffeners 
Design end connection 
Compute spacing of rivets for flanges 


For illustrating the operations, assume a plate girder as shown 
in Fig. 114. The span is 45'-0"; load 4000 pounds per lineal foot 
equals total load of 180,000 pounds; end shear 90,000 pounds; 

















138 


STEEL CONSTRUCTION 


maximum bending moment 12,150,000 inch-pounds. The shear and 
moment diagrams are given. 

Depth. Economy. For any set of conditions governing the 
design of a plate girder there is a depth which gives the greatest 
economy of metal. But there are so many conditions entering into 
the problem that no simple formula can be given for computing it. 


/S 0.000 U.O. 













. 4-6. 

4-0 

4-0 

,4-0 

,4-0 

4-0 

4-0 

4-0 

4-0 

4-0 

4-6 






45-Q 

•t 






30,000* 30,000 * 



.# 



The effects of some of these conditions can be stated in general 
terms as follows: 

The greater the shear the greater the depth required 

The greater the bending moment the greater the depth required 

The longer the span the greater the depth required 

The thicker the web plate the less the depth 

For lateral stiffness shallow depth is better 

The smaller the deflection allowed the greater the depth needed 




































































































































STEEL CONSTRUCTION 139 

If it is desired to determine the most economical depth for a 
given case, several depths must be assumed, the designs made, and 
the cross sections or weights computed. A few trials will lead to 
the desired result. 

The depth of the girder may be as small as of the span and 
may be as great as \ the span, but the usual range is tV to |. In 
the absence of any governing feature | of the span may be assumed 
as a suitable depth. 

Other Considerations. Usually other considerations than econ¬ 
omy will determine the depth. In building construction it is gener¬ 
ally desirable to make the girders as shallow as practicable, then the 
depth may be governed by deflection, by practicable thickness of 
web or section of flanges, or by details of connections. The final 
result must be determined by trial designs. 

In the example, Fig. 114, assume the depth of web plate to be 
48 inches. On account of the fact that the edges of the plate will 
not be exactly straight (unless they have been planed), it is custom¬ 
ary to set the flange angles \ inch beyond the edge of the plate, 
making the depth in this case 48| inches back to back of angles. 

Thickness of Web. In building work, inch is a suitable 
thickness to adopt as the minimum. For exceptional cases when 
the loads are light | inch may be used. Under Unit Stresses, 
p. 51, the allowable shear on girder webs is given, i. e., 10,000 
pounds per square inch. This is the average shear on the net 
cross section of the we£. In the example, Fig. 114, the maximum 

shear is 90,000 pounds; then the net area of the web must be 

or 9.0 square inches. The depth of the web is 48 inches, from which 
must be deducted 2 rivet holes f inch in diameter, making the net 
depth 46| inches. The thickness required to give the net cross 

section is - ^ ‘ 0 - or 0.19 inches. Hence a plate 0.19 inch thick fulfills 
46.25 

the requirements for shear on the web. This is less than the mini¬ 
mum adopted, so the thickness is made -jV inch. 

Problem - _ 

What thickness of web is required for a shear of 220,000 pounds, depth 44 

inches? 

Before the thickness of web can be accepted as being satisfac¬ 
tory, it must be known to provide ample bearing for the rivets which 




140 


STEEL CONSTRUCTION 


connect the flanges to the web. The design of this riveting is ex¬ 
plained later. For the present purpose the method used is this: 
Assume that an amount of stress equal to the maximum vertical 
shear must be transmitted from the web to each flange within a 
distance equal to the depth of the web. Applying this to the exam¬ 
ple, the maximum vertical shear is 90,000 pounds and this amount 
must be transmitted from web to flange in a distance of 48 inches, 
which equals the depth of the web. The bearing value of a f-inch 
rivet in a ^-inch web is 5860 pounds. The number required is 


90,000 

5860 


or 16. 


This number of rivets in a distance of 48 inches gives 


a spacing of 3 inches, which is satisfactory and requires only one row 
of rivets. (Two rows could be used, giving space for twice as many 
rivets as are needed.) Therefore, the web thickness is satisfactory. 

Shearing Value of Web Plates. A study of the shearing value 
of web plates compared with the bearing value of rivets in the web 
will show that sufficient bearing value can be developed to equal the 
shearing value. Consequently, the bearing test need not be applied. 
For a unit shear of 10,000 pounds per square inch and a unit bearing 
of 25,000 pounds per square inch, it can be shown that two rows of 
f-inch rivets, spaced 3f inches center to center in each row, will have 
the same bearing value as the shearing value of the plate (no reduc¬ 
tion being made in shearing value on account of rivet holes). 
Problem 

Assume a plate 64 inches deep and f inch thick. Prove the foregoing 
statement 

Moment of Inertia Required. Having the bending moment 
and the depth of the girder, the value of the required moment of 
inertia can be computed from the formula, (see p. 78). 


Me 

S 


In the example, Fig. 114, M = 12,150,000 in.-lb.; <8 = 16,000$. If 
no flange plates are used, the distance c is measured to the back of 
the angle, i. e., 24f inches. Then 


j 12,150,000X241- 

16,000 


18,415 


If it develops that flange plates must be used, the value of the moment 
of inertia must be increased to correspond to the increased depth. 





STEEL CONSTRUCTION 


141 


Flange Section. Having determined the moment of inertia 
required, it is next necessary to find by trial the section which has 
this moment of inertia. To avoid tedious figuring, a rough approxi¬ 
mation is first made. The web plate being determined, its moment 
of inertia may be computed or be taken from the handbook. 

I for PI. 48"X A" = 2880 


This amount deducted from 18,415 leaves 15,535 as the net value 
of / to be supplied by the flanges. The general formula for moment 
of inertia, p 38, is 

I = Ar 2 

15,535 


In this case r is about 22.5 inches, then r 2 = 506, and A = 

or 30.7 square inches. This is the net area 
of the two flanges. The gross section must 
be larger to allow for rivet holes; for this 
add 2.3 square inches, making 33.0 square 
inches, or 16.5 square inches for each 
flange. This area may be made up of 2 
angles without a plate or of 2 angles with a 
plate. Both cases are given. 

Case A—Without Flange Plates. With¬ 
out flange plates, use 2Ls 6"X6"X|", having 
an area of 2X8.44 or 16.88 square inches. 

For this case the total depth is 48| inches, 
as previously determined, and no correc¬ 
tion is needed for the required value of /, 
viz, 18,415. Now compute its value for 


.506 



the approximate section, Fig. 115, making - Fi s- Without 1 FianLfpiates irder 
the necessary corrections for rivet holes. 

1 PI. 48"XtV (from tables).2,880 

Deduct for holes 2XlX A X21.75X21.75 260 2,620 


1 = 


4 Ls 6X6X| (from tables) about axis a-a 113 
about axis b-b 4 X 8.44 X 22.47 X 22.47 17,045 

17,158 

Deduct for holes 4 X I X f X 21.75 X 21.75 1,241 15,917 

Total net value of I 18,537 

























142 


STEEL CONSTRUCTION 



In deducting for rivet holes, the diameter of hole deducted is 1 inch 
for a f-inch rivet. The distance to the holes is taken at the outer 
of the two rows of holes. 

The moment of inertia of the section is somewhat larger than 
the required amount, therefore the section is satisfactory. 

Case B—With Flange Plates. With flange plates it is usually 
specified that not less than one-half the flange area shall be in the 

angles, or the largest size, of angle shall be 
used. In this example it has been found 
that only one row of rivets is necessary for 
connecting flange to web. For the first 

trial use 2Ls6"X4"Xf" and 1 PI. 14"X T Y'. 
Then the gross area of one flange equals 

for 2 Ls 6" X 4" X f" 2 X 5.86 = 11.72 

for 1 PI.' 14"XtY = 6.12 

Total area =17.84 

The section is shown in Fig. 116. For this 
section the value of c is 24.25 + 0.44 or 
24.69. The required value of I must be 
corrected to correspond: 

, 12,150,000X24.69 lc „ n 

1 -i^ooo- 18 ’ 750 

I computed for the assumed 



5 fc & $ 
5 sj 


Fig. 116. Section of Plate Girder 
with Flange Plates 


The value of 
section is 


r 


1 = < 


1 PI. 48"X 

Deduct for holes 2X§X A X21.75x21 
4 Ls 6"X4"X|" about axis a-a 
about axis b-b 4X5.86X23.22X23.22 

Deduct for holes 
4X1X1X21.75X21.75 = 1036 
4X1X1X23.94X23.94 = 1260 

2 PI. 14" X tV less 2 rivet holes 
2 X 12j X tV X24.47 X 24.47 

Total net value of I 


=• 2880 
= 260 

= 30 

= 12,637 

2,620 

12,667 


2,296 

10,371 


= 6,418 
= 19,409 






























STEEL CONSTRUCTION 


143 


This value of 7 is in excess of the required value, the latter being 
18,750, hence the section may be reduced. The correction can be 
made without going through the calculations in detail. The angles 
need not be changed, but the flange plates may be reduced in thick¬ 
ness. By inspection it can be seen that a reduction of fa inch in 
thickness reduces 7 by 4 of 6418, or 917. The resulting net value 
of 7 is 19,409 — 917 or 18,492. This reduction in the thickness 
of the flange plate also reduces the required value of 7. It now 
becomes 


12,150,000X24.63 

16.000 


18.700 


These results are sufficiently close and the reduced section is used 
although it is somewhat scant. 

The revised section is 

web plate 48 "XtV 

f2Ls 6"X4"Xf 
\l PI. 14"Xf 

The sectional areas of the two designs are 


each flange 


1 PI. 48X A 

15.00 sq. in. 

4Ls 6X6X1 

33.76 sq. in. 


48.76 sq. in. 

1 PI. 48X A 

15.00 sq. in. 

4Ls 6X4X| 

23.44 sq. in. 

2 PI. 14xf 

10.50 sq. in. 


48.94 sq. in. 


This showing is slightly in favor of Case A, but it is more favor¬ 
able to Case B when it is considered that the flange plates do not 
extend the full length of the girder. Case B also has the advantage 
of greater lateral stiffness due to its greater width. On the other 
hand the cost of the additional riveting may amount to more than 
the saving in weight. Also the use of the flange plates, taking into 
account the rivet heads, increases the over-all depth about two 
inches, which may be objectionable in some cases. In general, the 
design without flange plates is preferred. 

Width of Flange Plates. The width of a flange plate is limited 
by the permissible projection beyond the outer row of rivets. The 
limits are eight times the thickness of the plate, or a maximum of 






144 


STEEL CONSTRUCTION 


six inches. In the above example this limit is 8Xf* or 3*. This 
permits a distance of 8 inches between the gage lines, which is 
satisfactory. 

The customary widths of flange plates vary by 2 inches, thus, 
10-inch, 12-inch, 14-inch, etc. For 6-inch flange angles the maxi¬ 




mum width is 20 inches, and for 8-inch angles, 24 inches, but 18 and 
20 inches, respectively, are preferable, and 14 inches and 18 inches 
are most used. When more than one plate is used on a flange, 
usually the outer one is made less in thickness than the inner one. 

Length of Flange Plates. The flange section which has just 
been computed is the section required at the place of maximum 
bending moment. The bending moment decreases toward the 
ends, as shown in the moment diagram Fig. 114, and, if it were 















































STEEL CONSTRUCTION 


145 


practicable to do so, the flanges might be decreased correspondingly. 
It is necessary for practical reasons to extend the flange angles the 
full length of the girder but the flange plates can be stopped at the 
points where they are no longer needed. The plate ceases to be 
needed at the point where the bending moment equals the resisting 
moment of the web plate and flange angles. This can be computed 
by the methods and from the data already given, but the process is 
tedious and the results can be obtained more easily by graphical 
methods with sufficient accuracy. 

Graphical Solution for Uniformly Distributed Loads. Let Fig. 
117-a represent the moment diagram for any uniformly distributed 
load. The lines at 1,2, 8, etc., represent the amount of the bending 
moment at the several points along the girder. The maximum 
bending moment is at 5. The resisting moment is represented by 
the line o c'. This line is divided into three parts, o a representing 
the resisting moment of the web plate, a b the resisting moment of 
the flange angles, and b c' the resisting moment of the flange plates. 
Then the distance a'a' equals the theoretical length of the flange 
angles, but practically they are made the full length of the girder, 
and b'b ' equals the theoretical length of the flange plates. If more 
than one plate is used on each flange, additional divisions may be 
made of the line oc', and the lengths determined in the same 
manner. 

If the resisting moments of the several parts of the flanges have 
not been computed, their moments of inertia may be used for this 
purpose in the following manner. On the edge of a sheet of paper 
or on a scale lay off at any convenient scale o a v a x b x , and b l c l 
equal, respectively, to the values of I for the web plate, flange 
angles, and flange plates. Hold the zero point at o and swing the 
paper or scale to the position where c x falls on the horizontal line 
through the apex of the moment diagram c'. Then the horizontal 
lines through a x and b x will cut the diagram at a' a' and b' b' and 
give the lengths of flange plates required. 

Graphical Solution for Concentrated Loads. Fig. 117-b repre¬ 
sents a moment diagram for concentrated loads. The same explan¬ 
ations and procedure apply as for uniformly distributed loads. 

Taking the girder section determined for Case B, p. 142, the 
length of its flange plates can be determined by the method just 


146 


STEEL CONSTRUCTION 


described, using the moment diagram in Fig. 114. The values of /, 


as computed on p. 143, are 

for web plate. 2,620 

for flange angles.10,371 

for flange plates. 5,501 

18,492 


Using a convenient scale lay off o c x equals 18,492, so that c t falls cn 
the horizontal line through c'. Then divide o c, at a t and so that 
oo, = 2620, cq ^ = 10,371, and b t <q=5501. Draw horizontal lines 
through a t and b v cutting the moment diagram at a' a' and b'b'. 
Then a' a' aiid b' b' represent the theoretical lengths of the flange 
angles and the flange plates, respectively. As previously stated, 
the flange angles always extend the full length of the girder. The 
flange plates are usually made two or three feet longer than theo¬ 
retically required. In this case the length b' b' is 23'-6" (approx.); 
the plates are made 26'-0" long. This extra length is used so that 
some stress can be developed in the plate at the points b' b'. 

Web Stiffeners. Schneider’s Specifications* provide “The web 
shall have stiffeners at the ends and inner edges of bearing plates, 
and at all points of concentrated loads, and also at intermediate 
points, when the thickness of the web is less than one-sixtieth, of 
the unsupported distance between flange angles, ^generally not 
farther apart than the depth of the full web plate, with a minimum 
limit of 5 feet.” 

The theory of stresses concerned in the design of stiffeners is too 
complicated for consideration in this text, but some simple rules can 
be established which will lead to safe construction. Web stiffeners 
may be divided into two distinct classes: (1) stiffeners at loaded 
points and (2) intermediate stiffeners. 

Stiffeners at Loaded Points. The chief purpose of stiffeners at 
loaded points is to transmit the loads to the girder web. According 
to the theory of stresses in girders, the load must be applied to the 
web and produce shear therein from which tension and compression 
are produced in the flanges. It is, therefore, necessary to carry the 
applied loads into the web plate as directly as possible. If the load 
is uniformly distributed on either the top or bottom flange, it is 

♦"The Structural Design of Buildings” by C. C. Schneider, M. Am. Soc. C. E., Transactions 
American Society .of Civil Engineers, Vol. LIV, p. 495. 







STEEL CONSTRUCTION 


147 


transmitted to the web by the rivets connecting the flange angles 
to the web. The effect of this load on the number of rivets required 
is considered later in the text. 

When concentrated loads are applied, enough rivets cannot be 
placed in the flanges to transmit the load to the web, and also it is 
desirable that the load be applied throughout the depth of the web 
plate. To meet these conditions stiffener angles are used. These 


J6Q OOO LBS 



Fig. 118. Details of Girder Showing Use of Stiffeners Under Concentrated Load 


stiffeners may be designed as short compression members using a 
unit stress of 12,000 pounds per square inch. They must be at¬ 
tached to the web plate with enough rivets to transmit the load. 
Generally the bearing value of rivets in the web plate will govern. 

As an example, assume that a girder supports a concentrated 
load of 160,000 pounds, Fig. 118. On account of the width of 
bearing of the load, it is desirable to use two pairs of stiffeners. The 



















































































































148 


STEEL CONSTRUCTION 


area required is ■ ’ or 13.33 square inches. 4 Ls 5*'X3j r X fa* 

12,000 

— area 4x3.53 or 14.12 square inches — provide the necessary 
sectional area. The thickness of the girder web being f inch, the 
bearing value of a f-inch rivet is 7030 pounds. Then the number 


of rivets required is 


160,000 

7030 


or 23. 


There is ample space for this 


number of rivets. 

The condition at the end bearing of a plate girder is analogous 
to that described for a concentrated load and is treated in the same 
manner. If the end of the girder connects to a column or another 
girder by means. of web -angles, the design is made in the same 
manner as for the web connection of I-beams. 

Intermediate Stiffeners. Intermediate stiffeners 
are used to prevent buckling of the web plate. Ac¬ 
cording to the specifications quoted above, stiffeners 
must be used if the unsupported depth of plate is 
more than 60 times its thickness. Such stiffeners 
are to be spaced not farther than the depth of the 
girder, or for deep girders not more than 5 feet. 
Applying .this to the girder illustrated in Fig. 118, 
it is found that stiffeners are required, for the unsup¬ 
ported depth is 36 inches, while 60 times the thick¬ 
ness f inch is 22\ inches. The depth of the girder 
is 4 feet, so the stiffeners are spaced 4 feet. 
Stiffeners, at loaded points serve incidentally to stiffen the web 
and are taken into account in spacing the intermediate stiffeners. 
Intermediate stiffeners are usually angles- in pairs. The leg of the 
angle parallel to the web plate need be only wide enough for rivet¬ 
ing, say 3 inches, as it adds but little to the lateral stiffness. The 
outstanding leg must be determined arbitrarily. For a 30-inch 
girder, 3 inches may be used; and for a 90-inch girder, 6 inches; and 
others in proportion. The thickness should be consistent with the 
size of the angle and not less than the thickness of the web plate; 
and the width of the outstanding leg should be somewhat less than 
the outstanding leg of the flange angles 

Stiffeners at loaded points must be ground to fit accurately 
against the loaded flange; intermediate stiffeners need not be so 



Fig. 119. Crimped 
Stiffeners 



















STEEL CONSTRUCTION 


149 


carefully fitted. The use of fillers under stiffener angles is not 
necessary, but a better fit can be obtained when they are used. 
This makes it desirable to use them at loaded points and end bear¬ 
ings. Where fillers are not used, the stiffener angles must be crimped 
to fit the flange angles, Fig. 119. There is little difference in cost, 
as the expense of crimping offsets the cost of the filler plates. 

Refer to the girder in Fig. 114. There being no concentrated 
loads, stiffeners at loaded points are required only at the end bearings. 
The reaction at each end is 90,000 pounds. The area of stiffener 

angles required is or 7.5 square inch. 4 Ls 3^X3"X have 

sufficient area, but it is desirable to have them approximately as 
wide as the flange angles, so 4 Ls 5"X3"X ft" are used. Sixteen 
rivets are required. There is ample space for them. 

The web plate is inch thick and has an unsupported depth 
of 36 inches, hence it requires intermediate stiffeners. These are 
spaced about 4 feet apart (equal to the depth of the girder). Angles 
4"X3"X is" may be used for these stiffeners. 

Rivets Connecting Flange Angles to Web. In order to make 
the several pieces of the plate girder act as a unit, they must be 
rigidly connected. It is evident that if the angles and plates were 
simply placed in their relative positions without being riveted, they 
would not co-operate but would tend to act independently. This 
is explained under Horizontal Shear in “Strength of Materials/* 
Part II. 

Number of Rivets. The loads on the girder are applied either 
directly or indirectly to the web, producing vertical shear. By 
flexure, the vertical shear produces horizontal shear, which becomes 
tension and compression in fibers below and above the neutral axis, 
respectively. Most of these stresses occur in the flange plates and 
angles and must be transmitted to them from the web by the rivets 
which connect the angles to the web plate. There must be enough 
rivets to transmit the whole amount of the stress and they must be 
located at the points where the stress should pass from the web to 
the flanges. Then in each flange there must be such a number of 
rivets between the point of maximum flange stress (maximum 
moment) and each end to transmit the total flange stress; or, stated 
in other terms, the resisting moment of the rivets between the point 



150 


STEEL CONSTRUCTION 


of maximum bending moment and each end must equal the maxi¬ 
mum bending moment, and this equals the resisting moment of the 
girder section. 

In Fig. 118, let d be the average distance between the rivets in the 
top and bottom flanges; k the bearing value of one rivet (usually bear¬ 
ing in the web plate); M the bending moment in inch-pounds; and N 
the number of rivets in one end of one flange. Then kXd equals the 

M 

resisting moment of one pair of rivets in inch-pounds and 

equals the number of pairs or the number of rivets in each flange 
from the center or point of maximum bending moment to either 
end. For example, assume the following data: 


M = 450,000 ft.-lb. = 5,400,000 ih.-lb. 
k =7030$, bearing value of a f-inch rivet in a f-inch web 
d —41" 


then 


\t _ 5,400,000 
7030X41 


= 19 rivets 


Rivet Spacing in Flanges. If the rivets, Fig. 117-a and -b, were 
spaced uniformly, their resisting moment would be represented by the 
moment diagram o' c' o', whereas, the bending moment diagram is 
o' a' b' c' b' a' o'. From this it is clear that the resisting moment of 
the rivets is less than the bending moment at all points except at the 
maximum. But these rivets can be so spaced that the two moment 
diagrams will coincide. To determine this spacing proceed as 
follows: Lay off oN equal to the total value of the number of rivets, 
say 19, and divide it into 19 spaces at the points s. Through the 
points s, draw horizontal lines intersecting the moment diagram at 
points t. Through the points t, draw vertical lines intersecting the base 
line at the points r. Then the points r are the locations of the rivets. 

It is important to note that the rivets are closer together near 
the ends, i. e., where the bending moment is changing rapidly. On 
the left side of Fig. 117-b, the spaces are nearly equal because this 
side of the moment diagram is nearly a straight line. There is a 
change of spacing wherever there is a change in direction of the 
moment diagram. For the uniform load, Fig. 117-a, there is a 
change in each space. Of course it is not practicable to space the 
rivets strictly in accordance with the theory. The practical method 




STEEL CONSTRUCTION 


151 


is to divide the girder into sections, usually taking the divisions 
formed by the stiffeners, and space the rivets equally in each division. 

In the problem, Fig. 114. use the following data: 

M = 12,150,000 in.-lb. 

k =5800$, bearing value of a f-inch rivet in a &-inch web 
d =41.26" (Case A, Fig. 115) 


then 


12,150,000 

5860X41.26 


— 50 rivets 


Lay off oN equals 50. Along o o' lay off the points 1, 2, 3, 
etc., marking the positions of the stiffeners. Through these points 
draw verticals intersecting the moment diagram at t v t 2 , etc.; thence 
draw horizontals intersecting o N at s v s 2 , s 3 , etc. Then o repre¬ 
sents the number of rivets between o and 1 ; s 2 , the number between 

1 and 2\ s 2 s 3 the number between 2 and 3\ etc. 

o represents 17 rivets; the distance o'-l is 54 inches; space the 
rivets 3 inches center to center. 

5, s 2 represents 14 rivets; the distance 1-2 is 48 inches; space 
the rivets 3£ inches center to center. 

s 2 s 3 represents 10 rivets; the distance 2-3 is 48 inches; space the 
rivets 4^ inches center to center. 

s 3 s t represents 7 rivets; the distance 3-4 is 48 inches; space the 
rivets 6 inches center to center, and this being the maximum spacing 
allowed, continue it to the center of the span. 

If Case B be used, the procedure is just the same. The value 
of d would be larger (Fig. 116) and, consequently, the number of 
rivets smaller. 

Riveting for Cover Plates. In Case B there must also be deter¬ 
mined the necessary riveting for attaching the cover plates to the 
flangfe angles. The procedure is similar to that just given. In 
Fig. 114, p c' represents the resisting moment of the cover plates and, 
therefore, the required resisting moment of the rivets. The rivets 
are in single shear, and the moment arm is the distance back to 
back of flange angles. Use the following data: 

M = 3,600,000 in.-lb. (approx.). 
k =4420#, single shearing value of a f-inch rivet 
d = 48§" (Fig. 116) 


Then 


, r _ 3,600,000 
“48^X4420 


= 17 rivets 




152 


STEEL CONSTRUCTION 


Lay off p equals 17. Along b' b' lay off the points 10, 11, 
etc., at intervals of say 4 feet. Draw verticals to / I0 , /,,, etc., and 
horizontals to s l0 , s u , etc. 

p s 10 represents 9 rivets; the distance b'-lO is 48 inches. There 
are two rows of rivets in the flange plate, so there are 4| rivets 
required in one row in 48 inches, i. e., spaced about 10 inches, center 
to center. But the maximum allowable spacing is 6 inches, center 
to center, and this is used throughout the length of the cover plates 
except at the ends where a spacing of 4 inches for a distance of two 
feet is adopted arbitrarily. 

Rivet Spacing Computed f rom Web Bearing. The method, p. 140, 
for checking the thickness of the web plate for rivet bearing may be 
used for determining the rivet spacing; for example, assume that an 
amount of stress equal to the vertical shear must be transmitted from 
the web to each flange within a distance equal to the depth of the web. 
Then the number of rivets required in this distance is determined 
by dividing the vertical shear by the bearing value of one rivet. 

Referring to Fig. 114 and applying this method: 


Shear at O' = 90,000 # 
No. of rivets in 48" 


90,000 

5860 


16, spacing about 3" 


Shear at 1 =72,000# 
No. of rivets in 48" 

Shear at 2 = 56,000 # 
No. of rivets in 48" 

Shear at 3 =40,000# 
No. of rivets in 48" 


72,000 

5860 

56,000 

5860 

40,000 

5860 


13, spacing about 3^" 
10, spacing about 4^' 
7, spacing about 6" 


Spacing when Load Transmitted through Flange Rivets into Web. 
If the load on the girder is applied in such a way that it must be 
transmitted through the flange rivets into the web, then the rivet 
spacing must take this into account. The exact method of doing 
so is difficult to apply, but safe results can be obtained by simply 
adding enough rivets to transmit the load to the web. Thus in Fig. 
114 it has been determined that 17 rivets are required between o'-l. 
The Load on this space is 18,000 pounds, which requires 4 rivets to 
transmit it into the web plate. Then the total number of rivets is 
21 and the spacing 2\ inches. 






TOT ML LENGTH 


STEEL CONSTRUCTION 


153 



■O 

u, 

5 

0> 

c3 

E 

O 

M 

a 

*£ 

c3 

c 

Q 

a 

W) 

'S3 

<v 

Q 


© 

<N 


bD 

E 


Assuming that the 
load is applied on the top 
flange, the extra rivets are 
required only in. that 
flange. But in practice 
the riveting is usually 
made the same in both 
flanges. Where stiffeners 
are used at loaded points, 
the extra rivets are not 
required. 

The actual location 
and spacing of the rivets 
must be worked out in 
making the shop details 
in order to afford neces¬ 
sary clearances from stiff¬ 
eners and to suit any , 
other conditions that 
may apply to the case. 
It is sufficient for the de¬ 
signer to indicate the 
spacing as it has been 
computed above. 

Fig. 120 shows the 
design drawing for the 
girder developed in the 
preceding pages, using 
Case B, that is, a girder 
with flange plates. 
Problems 

1. Design a plate girder 
from the data given in Fig. 
121. Make the design draw¬ 
ing at f-inch scale. 

2. Design a plate girder 
having the same span as the 
one in Fig. 121, but support¬ 
ing only one-half the load 
there specified. 








































































































































































154 


STEEL CONSTRUCTION 


Tables and Diagrams. A number of tables have been pub¬ 
lished giving strength and properties of plate girders. These tables 



are of much assistance in arriving at the approximate section of the 
required girder, but usually the final design must be computed in 
detail, as in the foregoing example. 



After Deducting Rivet Holes. 2 Holes, (%" Rivets) for 

The large number of plate girder sections that it is possible to 
make up from the available sizes of web plates, flange angles, and 
flange plates makes it impracticable to have complete tables of them. 
The Carnegie Pocket Companion, 1913 edition, contains a valuable 
























































































































































































































































































































































































STEEL CONSTRUCTION 155 

table giving the section modulus for a large number of riveted 
girders. 

The handbooks give tables of the moment of inertia of rectangles 
from which can be taken the value of I for the web plate (from 
this value must be deducted the value of I for rivet holes). Other 
reference books give the values of / for web plates with rivet holes 
deducted and for many sizes of flange angles placed at various 
depths; similar tables are given for flange plates. By the use of 
these tables, the value of I for the complete girder section can be 
found by adding together the values for the web plate, flange angles, 
and flange plates.* 

Ihe diagrams, Figs. 122, 123, and 124, give respectively, the 
values of I for w r eb plates, flange angles, and flange plates. They 
give the moments of inertia for the sizes of plates and angles most 



to i" Plates; 2 Holes, 1" Q" Rivets) for f " to 1" Plates 

commonly used for plate girders. Values for intermediate sizes of 
plates and thicknesses of angles can be interpolated. Although not 


♦“Godfrey’s Tables” by Edward Godfrey, M. Am. Soc. C. E. 

“Civil Engineer’s Pocketbook’’ by Albert 1. Frye, S. B., M. Am. Soc. C. E. 


































































































































































































































































































































MOMENT OF INERTIA 


156 


STEEL CONSTRUCTION 


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Fig. 123. Diagram for Determining Moments of Inertia of Flange Angles of Plate Girders 

































































































































































































































































































































































































































































































































MOMENT Or INEHTlA 


STEEL CONSTRUCTION 


157 



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Fig. 124. Diagram for Determining Moments of Inertia of Flange Plates of Plate Girders 











































































































































































































































































































































































































































































































































































































































































158 


STEEL CONSTRUCTION 

mathematically exact, the results obtained from these diagrams are 
accurate enough for designing, and will lead to the selection of the 
same sections as would be determined by computation. 

The tables and diagrams give only the sections to be used for 
the girder. The flange plate length, stiffeners, end connections, 
and rivet spacing must still be designed by the methods heretofore 
explained. In many cases, these latter items are left to the de- 
tailers; but they are properly a part of the design and should be 
worked out at the same time the girder section is determined, as 
the detailer is not likely to have as clear an understanding of the 
conditions as the designer. 

Problem 

Check the girder sections in Figs. 115 and 116 by means of the diagrams in 
Figs. 122, 123, and 124. 

OTHER FORMS OF RIVETED GIRDERS 

The discussion and examples thus far have dealt with the plate 
girder. The principles and the methods involved are the same for 
all forms of riveted girders. 

I=Beams with Flange Plates. A form of girder, Fig. 111-a, is 
used when shallow girders are required and the I-beams are not 
strong enough. This often occurs in joists and girders of a floor 
when it is desired to maintain approximately the same depth for 
members which carry heavy and light loads. 

Moment of Inertia. To determine the moment of inertia of the 
girder, take from the handbook the value of I for the beam and 
deduct therefrom the value of I for the holes in the flanges; add to 
this net value for the beam, the value of I for the net section of the 
flange plates. For example compute the moment of inertia for 
15" I 42# and 2 PI. S"Xf. 

7 for 15" I 42# 442 

deduct for 4 rivet holes 
4X|X|X7.2X7.2 > 114 

328 

for 2 PI. 8"Xf" after deducTing rivet holes 

2X6|Xf X7.9X7.9 585 

Total value of I 913 

Note that two rivet holes are deducted from each flange and from 
each plate. If the rivet holes are carefully staggered, only one-half 



/ 


STEEL CONSTRUCTION 


159 


Table iv 

Moments of Inertia of I=Beams with Holes in*Flanges 


(Holes for 3 rivets computed diam.) 


SECTION 

MOMENTS OF INERTIA 

Grip, or Thick 
i.ess of Metal 
at Hole 

Whole 

1 Hole Out of 
Each Flange 

2 Holes Out ot 
Each Flange 

27 "I 

83# 

2SSS.6 

2623.0 

2357.4 

.89 

24"I 100# 

2380.3 

2149.0 

1917.7 

1.00 

24"I 

80# 

2087.9 

1884.9 

1681.9 

.87 

24"I 

69-1# 

1928.0 

1734.3 

1540.6 

.82 

21 "I 

571# 

1227.5 

1090.0 

952.5 

.74 

20"I 

80# 

1466.5 

1320.0 

1173.5 

.92 

20"I 

65# 

1169.6 

1042.4 

915.2 

.79 

1ST 

75# 

1141.3 

1026.8 

911.3 

.90 

1ST 

55# 

795.6 

704.9 

614.2 

.69 

1ST 

36# 

733.2 

645.2 

557.2 

.67 

15"I 

80# 

795.5 

706.6 

617.7 

1.03 

15"I 

60# 

609.0 

536.6 

464.2 

.82 

15'T 

42# 

441.7 

385.3 

328.9 

.62 

15"I 

36# 

405.1 

351.8 

298.5 

.59 

12" I 

40# 

268.9 

231.3 

193.7 

.66 

12"I 

311# 

215.8 

184.5 

153.2 

.545 

12"I 

271# 

199.6 

169.9 

140.2 

.51 

10'T 

25# 

122.1 

102.7 

83.3 

.49 

9 "I 

21# 

84.9 

70.2 

55.5 

.46 

8"I 

is# 

56.9 

46.1 

35.3 

. 425 


of this number need be deducted. The shearing value of the web 
must be investigated and the length of flange plates and rivet spac¬ 
ing computed in the same manner as for plate girders: 

Problems 

1. What is the resisting moment of a girder made of one IS" I 55# and 
two flange plates 8"XT? 

2. A beam has a span of 24 feet and supports a u. d. load of 80,000 pounds. 
Design the beam using a 18" I 55# with flange plates. Determine lengUi of 
plates and rivet spacing. 

3. What is the resisting moment of a 20" I 65# with two I-inch holes in 
eachflange? (Note the great loss of strengthdue to punching holes in the flanges.) 

The moments of inertia of I-beams with holes in the flanges are 
given in Table IV and of flange plates in the diagram, Fig. 123. 

Beam Box Girders. Beam box girders, Fig. 111-d, are designed 
in just the same way as single I-beams with flange plates. They 
are not economical and should be used only when the available 

















160 


STEEL CONSTRUCTION 


depth prevents the use of a deeper girder. The handbooks give 
tables of strength of this form of riveted girders. 

Problems 

1. Compute the moment of inertia of a girder made of two X-beams 
24'X80# and two plates 18'Xf". 

2. Design a beam box girder to support a load of 300,000 pounds at the 
middle of a 30-foot span. Use 24-inch beams. 

3. What is the resisting moment of a girder made of two 15" Cs 33# and 
two plates 14'X W? 

Plate Box Girders. The plate box girder, Fig. 111-c, needs no 
explanation as to the method of design, requiring the same procedure 
as the plate girder. It is used for very heavy loads when the depth 
allowed is greater than the deepest I-beam but not sufficient to per¬ 
mit the use of a girder w ith a single web. It is to be noted that the 
rivets connecting the flange angles to the webs are in single shear, 
hence the shearing value rather than the bearing value of the rivets 
will be used in computing rivet spacing. 

Problem 

Compute the moment of inertia of a girder made of two web plates 36' X Yi , 
four angles 6'X6'X two flange plates 22' X|', and two flange plates 22' X . 

UAsymmetrical Sections. Thus far in the discussion of riveted 
girders the sections considered have been symmetrical about the 
neutral axis and, therefore, the neutral axis has been at mid-depth. 
It sometimes happens that the two flanges cannot be the same. 
This makes the computation of the moment of inertia more difficult. 
Having made the first approximation of the section, it is necessary 
to find the center of gravity of the assumed section, p. 35, and then 
the moment of inertia about the neutral axis (through the center 
of gravity), p. 36. 

The common examples of unsymmetrical sections are crane 
girders, I-beam lintels with one flange plate, girders requiring extra 
lateral stiffness on account of unsupported top flange, and I-beams 
with rivet holes in the tension flange at the place of maximum 
bending moment. 

In designing such girders the flanges are made as nearly equal 
as practicable, so that the neutral axis may be near mid-depth. 
Of course this cannot be done when a single flange plate is used on 
an I-beam. With the exception noted above, viz, locating the 



© 


G? OPPOSITE HAND EXCEPT PLATES pa OMITTED SECT I OH 

Fig. 125. Shop Detail Drawing of Girder, the Design Drawing of Which Is Shown in Plate 0 























































































































































































































£ PIER 


162 


STEEL CONSTRUCTION 



neutral axis, the procedure in 
designing is the same as for 
symmetrical girders. 

Problems 

1. A lintel is made of a 12" I 
31and a plate on the top flange 
12" X rs". What is the moment of 
inertia of the section? 

2. What is the resisting mo¬ 
ment of a 15" X 42# which has two 
holes for f-inch rivets in the bottom 
flange? 

PRACTICAL APPLICATIONS 

Girder Supporting a Col¬ 
umn. In order to get the 
rooms in the lower part of a 
building arranged satisfacto¬ 
rily, it is sometimes desirable 
to space the columns differ¬ 
ently than they are placed 
above. This makes it neces¬ 
sary to carry the upper col¬ 
umns on girders. Such a case 
is shown in Plate O, p. 285. 
As is usual in such cases, the 
amount of vertical space avail¬ 
able is limited and the depth 
of the girder is fixed by other 
considerations than economy 
of design. The top is limited 
by the floor level above, it 
being necessary to have room 
for fireproofing and for the fin¬ 
ished flooring. The bottom is 
limited by the clearance re¬ 
quired for the floor below. The 
actual depth of web is de¬ 
termined after making a pre- 



































































STEEL CONSTRUCTION 


163 


liminary design of the flanges and finding the approximate thickness 
of flange plates. 


p 








L 






c 

c 

3 

5 

d 








-i 









_ PANEL L OAD /OX/9%80*-15,200 


■ 

; 

X I I I I 


1 

A*"- 

i 

H 


Fig. 127. Girder for Garage Roof 


The vertical shear is so large that a single 
web plate would have greater thickness than is 
desirable and, furthermore, the shape and posi¬ 
tion of the supporting columns would make the 
connection of a single girder somewhat difficult to 
design. This leads to the adoption of two web 
plates. 

At the supporting columns it is desired to 
connect one web plate to each flange of the col¬ 
umn as shown. If a box girder were used, it 
would be difficult to erect it, hence two girders 
best fulfill the conditions. Having settled the 
above points, the girder is designed by the meth¬ 
ods which have been given. Plate O shows the 
design drawing of the girder and Fig. 125 is the 
shop detail drawing. 

Problem 

In the first story of a building it is necessary to omit 
a column and support the upper part of the column on a 



Fig. 128. Section of 
Typical Crane Girder 






















































164 


STEEL CONSTRUCTION 


girder. The span of the girder is 36 feet. The load is 540,000 pounds applied 
at the center of the span, and in addition to this there is a u. d. load from the 
second floor, the weight of girder with its fireproofing amounting to 4200 
pounds per lineal foot. The depth available is 50 inches. Design the cross 
section of the girder. 

Plate Girder Lintel. Fig. 12G shows a plate girder used as a 
lintel over a driveway into a building. It supports the wall above 
and the floor loads which bear on the wall. 


Roof Girder. A garage roof is to be built with no supporting 
columns, so it must be carried from wall to wall on girders. The 



Fig 129 Plate Girder Bearing od Masonry Fig. 130 Diagram Showing Web Connection of 

Girder to Column 


are connected to the girders. The dimensions and loads are given 
in Fig. 127. There is no limitation of depth, the most economical 
section being desired. 

Problem 

Design the girder for the conditions given above and make design drawing 
at f-inch scale. 

Crane Girders. Crane girders do not belong to the class ol 
buildings now under consideration. Fig. 128 represents a tvpicai 
crane girder and is given to illustrate the use of an unsymmetrical 















































STEEL CONSTRUCTION 


165 


section of girder. The stresses in a crane girder and the design are 
explained under Runway Girders in “Roof Trusses”. The channel 
on the top flange is required to give lateral stiffness to the girder in 
order to resist the lateral thrust of the crane when the carriage is 
moving crosswise of the build¬ 
ing. It also serves incidentally 
as a guard rail. 

Problem 

Locate the neutral axis of the 
girder illustrated in Fig. 128. 

DETAILS OF CONSTRUCTION* 

End Bearings. When the 
end of a girder bears on ma¬ 
sonry, Fig. 129, the bearing plate 
is designed in the same manner 
as for beams. With riveted 
girders it is much more fre¬ 
quently necessary to replace 
the plain bearing plate by I- 
beams to spread the bearing 
along walls, than when the 
girder is an I-beam'. A sole 
plate should be riveted to the 
bottom of the girder. It stiffens 
the flange angles and furnishes 
a more even bearing surface 
than the angles. In high-grade 
work, the bottom of the girder 
may be faced before the sole plate is attached. 

A very heavy load may require a bearing plate thicker than it is 
practicable to obtain. Then, if it is not desired to use I-beam grill¬ 
age, a cast-iron pedestal may be used similar to those used for 
columns. The method of designing them is given under columns, 

p. 220. 

Problem 

Design the end bearing for the girder specified in Fig 114. 



Fig. 131. 


Diagram Showing Bracket Connection 
of Girder to Column 


♦The details of stiffener angles, filler plates, flange plates, and rivet spacing have been dis¬ 
cussed and illustrated in the preceding pages. 



























































166 


STEEL CONSTRUCTION 


v Connections to Columns. Web Angle Connection. The con¬ 
nection of a girder to a column is usually made with web angles. 
The connection is designed in the same manner as for I-beams. The 
angle legs connecting to the girder web should be wide enough to 



take two rows of rivets and, if the construction is heavy, the filler 
plate should be wide enough to take a row of rivets beyond the 
edge of the angles, Fig. 130. The end angles must be set accurately 
to the correct length and at right angles to the axis of the girder. 
In railroad bridge construction the end angles are required to be 
faced and, to allow for it, the angles used are | inch thicker than 



































































































































STEEL CONSTRUCTION 


167 


otherwise would be required. This should be done on heavy work 
in building construction. 



0 0 0 0 

0 0 0 0 0 0 - 00-0 0 

0 0 0 0 ) 

> 0 0 0 0 

0 000-010 0 000 

0 0 0 0 0 ) 

> t $ f ^ 

0 0 0 0 0-10 0 0 0 0 

0 0 0 0 0 

1 0 $ 0 $ 

00 00-0 |_00000 

0 0 0 0 ( 


(a) 5PL ICC III FLANGE PLATE 



(6) SPLICE IN EL ANGE ANGLES 


00000 000001000 00000 00 

000 0. 000000 | 000000000 


00000J0000 0 
00000 | 00000 

0 ppl . sy,f 

• 

WEB PL. t&jF' 

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0|0 

*«!<!> <t ' 
%!♦* 

p epl iax,f 


0 0 0 0 0 j -0 -<j>—0—0 -0 

0 0 0 0 -0|-0 0 0-0—0- 

oppl. 6"xf e “ 

(>000000000 i 000000000 4 

000000 0000J0000 0 00000 


( C ) SPLICE IN WEB PLATE. 

Fig. 133. Diagrams of Splices in the Members of a Plate Girder Section 


Bracket Connection. The bracket connection, Fig. 131, may 
be used. It does not make as stiff a joint as the web connection and 
should not be used unless there is some special reason for it. This 



























































































168 


STEEL CONSTRUCTION 


type of connection is specially applicable to box columns on which the 
brackets must be riveted before the column is assembled. Other 
forms of connection may be used to meet special conditions. 
Fig. 132 shows a connection of the web directly to the face of the 
column. 

Splices. It is self-evident that there should be no splice in a 
girder section or in any of its members unless such a splice is abso¬ 
lutely necessary. If the splicing is of individual members rather 
than the whole girder section, the extra work is done at the shop 
instead of in the field and, therefore, is not so serious. 

Splicing Due to Transportation Difficulties. The splicing of an 
entire girder section may be occasioned by transportation condi¬ 
tions but it is expensive on account of extra material and field 
riveting required, and cannot be considered as good as the unspliced 
section. A girder of any length likely to occur in building construc¬ 
tion can be shipped by rail, so that the matter involves only the 
comparison of the extra freight cost w r ith the cost of the splice. 
But transportation by boat involves not only the extra charge for 
long members but an absolute limit to the length that can be stowed. 
The designer, if not familiar with freight rates and rules, must inves¬ 
tigate them, if girders longer than 36 feet are to be shipped. 

Splicing Due to Members Longer than Stock Sizes. The individual 
members of a girder may need splicing, due to inability to secure 
material of sufficient length, which often happens when material 
is ordered from stock. This indicates the desirability of consulting 
stock lists while designing, so that the available sections may be 
used. The rolling mills regularly furnish angles 60 feet long and by 
special arrangement will furnish longer lengths. All usual sizes of 
cover plates are furnished in lengths up to 85 feet. Web plates are 
most likely to require splicing. Lists of extreme sizes are given in 
the handbooks. Greater lengths than there listed can be secured 
from some mills, but it is safer to be governed by these lists unless 
definite arrangements can be made for the longer plates. 

Full Strength Splices for Flanges. Both tension and compres¬ 
sion flanges must be fully spliced, i. e., the entire tension or com¬ 
pression must go through the splice plates and angles and the rivets 
by which they are attached. In this case no reliance is placed on 
abutting ends of compression members as is done in columns. 


STEEL CONSTRUCTION 


169 


Figs. 133-a, -b, and -c show, respectively, splices in a flange 
plate, in flange angles, and in web plate. 

Splice for Flange Plate. Fig. 133-a. The flange plate is 14" X 
The stress must be carried across the gap by a single plate (assum¬ 
ing that there is no unused capacity in the flange angles), which must 
not be less than 14" X^". The net area of this plate after deducting 
rivet holes is 12j"x|" or 6.125 square inches. Its tensile value is 
6. 125X1 6,000 or 98,000 pounds. The splice rivets are in single shear, 

hence the number required on each side of the joint is or 19. 

Use 20 rivets. 

Splice for Flange Angles. Fig. 133-b. The flange angles are 2 
Ls 6"X6"X|". Their area is 2x7 11 or 14.22 square inches, which, 
after deducting one rivet hole from each angle, becomes a net area of 
13.12 square inches. The splice plates must have this net area. It 
is desired to splice both legs of each angle as directly as possible, 
so the splice plates are arranged as shown. Their sizes and net 
areas are 

m 2 PI. 5" X net area 6 18 
n 1 PI. 13"X§", net area 7.03 

Total 13 21 sq. in. 

From these values the number of rivets can be computed in the 
usual way, noting that the rivets through m are in double shear and 
through n in single shear. The plates m must extend beyond n at 
each end far enough to take two additional rivets. The purpose of 
this is to relieve the angles of a portion of their stress before the first 
holes in n are reached. Otherwise, in designing the main girder 
section one hole additional would be deducted from each angle. 

Splice for Web Plate. Fig. 133-c. The web plate must be spliced 
to transmit shear and bending according to the amount of these 
stresses where the splice occurs; if at the place of maximum bending 
moment, only the bending stresses need be considered, shear being 
zero; if near the end where the flange angles will take care of all the 
bending stresses, then only the shear need be provided for. 

Resistance to bending. The necessary resistance to bending 
can be furnished by a flange plate, as in Fig. 133-a; by splice plates 
on the angles, as plates m in Fig. 133-b; or by splice plates o in Fig. 




170 


STEEL CONSTRUCTION 


133-c; or by any combination of them. In either case the moment 
of inertia of the net section of the splice plate must equal that of the 
web plate, or such portion of it as is needed at the place where the 
splice occurs. It must be noted that a web plate which must be 
spliced loses some of its moment of inertia because of the holes for 
attaching the splice plates; consequently, it is better, if practicable, 
to use a form of splice which will add no rivet holes. If a flange 
plate is used as a part of the girder section, then an additional flange 
plate may be used for splicing the web. If there is no flange plate 
in the girder section, then plates such as m, Fig. 133-b, may be used 
to advantage for all or part of the web splice. 

Taking for example the girder in Fig. 116, the web plate is 48" 



Fig_ 134. Splice in Plate Girder Fig. 135. Bracket lor Bracing 

Top Flange of Girder 


X h"■ Its net moment of inertia is 2620, p. 141. Two flange plates 
14" Xf" after deducting 2 rivet holes from each, have a net value of I 
I = 2xl2jXsX24 9X24.9 = 3800 
which is more than required. 

Taking the girder shown in Fig. 115, if a flange plate should be 
used for splicing, the angles would be weakened by the rivet holes 
for attaching the plate. If plates such as m, Fig. 133-b, are used, 
no additional rivets are needed. Try four plates 5"Xf". Their net 
value of 1 after deducting one rivet hole for each is 

7 = 4x4| X|X20^X20^ = 2600 ‘ 

which is near enough to be satisfactory. 























































STEEL CONSTRUCTION 


171 


OtrfDER 


In a similar manner, plates o, Fig. 133-c, are found to be G"X 
The strength ot the spliee plate must be developed by rivet bearing 
in the web plate requiring 10 on each 
side of the joint. Although this is the 
most direct method of splicing for bend¬ 
ing, it is not as economical as either of 
the other methods given above. 

Resistance to Shear. For resisting 
shear, the splice plates are in the form of 
the plates p, Fig. 133-c. On each side of 
the joint there must be enough rivets to 
transmit the total shear. They may be 
in one or more rows. The thickness of 
each plate must be at least half that of the web plate and is sub¬ 
ject to the same minimum. Hence, in this case the thickness is 
made ts inch. 



Fig. 13G. Brace for Plate Girder 



Position of Splices. Girders completed in the shop will have splices 
arranged to come at different places; thus the web may be spliced at 
the center and the angles near one end; still better, one angle may be 
spliced on one side of the center and the other on the opposite side. 
Of course, in a field splice all the elements are joined at one place. 
The method of computing is the same as has been given for the 
individual parts of the girder (bearing in mind that the rivets are 
































172 


STEEL CONSTRUCTION 


field driven). Fig. 134 illustrates such a splice made up from the 
several splices shown in Fig. 133. 

* 

Problem 

Design field splice for plate girder shown in Fig 115. 

Lateral Support. Girders, like beams, must be supported later¬ 
ally to prevent the compression flange from buckling. Schneider’s 
Specifications provide that “the unsupported length of flange shall 
not exceed 16 times its width. In plate girders used as crane run¬ 
ways, if the unsupported length of the compression flange exceeds 
12 times its width, the flange shall be figured as a column between 
the points of support.”* 

In most cases the lateral support is provided by the joists or 
floor construction. Where this is not the case, the supports can be 
provided in a number of different ways. For lengths up to 25 feet, 
the necessary stiffness can be provided by the use of wide flange 
plates. For greater lengths, box girders may be used, if the load 
warrants their use. Fig. 135 shows a plate girder to which a joist 
connects near the bottom. From this joist a bracket extends up to 
and supports the top flange. The corner brace indicated in Fig. 
136 sometimes may be used to advantage. 

As provided in Schneider’s Specifications, crane girders whose 
length exceeds 12 times the width must be designed as columns. 
The method is the same as given hereinafter for columns. 

The ends of the girders must be especially well secured against 
overturning. When connected to columns or other girders, the 
desired result is easily attained by the use of web angles or top con¬ 
nection angles. If the end rests upon and is built into masonry', the 
required support is thus provided. Fig. 137 shows one girder rest¬ 
ing on another and braced thereto. 


* Transactions American Society of .Civil Engineers, Vol. LIV, p. 49;,. 









MONROE BUILDING, CHICAGO 

Holabird & Roche, Architects 












STEEL CONSTRUCTION 


PART III 


COMPRESSION MEMBERS—COLUMNS 
STEEL COLUMNS 

Definitions. A column (or strut ) is a member subjected to 
compression in the direction of its longitudinal axis, i. e., subjected 
to axial compression. The term “column’’ is usually applied to a 
vertical member subjected directly to a gravity load. The com¬ 
pression members of trusses, and also small isolated members, and 
members in other than the vertical position, are called “struts” 

A series of columns in a vertical line is called a “stack”. 

The columns in any one story of a building constitute a “tier”. 

Loads and their Effects. Computation of Loads. The loads on 
a column are applied to it by the column section above and through 
the connections of other members or other materials. Most com¬ 
monly this is through beams and girders. The amounts of these 
loads may be taken from those,previously computed for the beams 
and girders, or may be computed directly from the floor and wall 
areas tributary to the column. The former method is easier when 
the loads and areas are irregular, and the latter when the loads are 
uniform and the arrangement of beams regular. Practical exam¬ 
ples of computing the loads are given later in this book. 

The ideal condition of loading of a column is had when the load 
is applied uniformly over the top of a column, and when the bottom 
of the column bears evenly on its support or foundation. In a 
stack of columns, the load on any column which comes from the 
column above is usually applied in this ideal way. But the other 
loads are generally applied to the sides of the column through beam 
connections, in many cases with greater loads on one side than on 
the other. 




174 


STEEL CONSTRUCTION 


Loads applied centrally, or which are equally balanced on oppo¬ 
site sides, are called “concentric loads”, Fig. 138-a. Loads applied 

to the sides of the column and not balanced, 
or those which bear on top but are not cen¬ 
trally placed, are called “eccentric loads”, 
Fig. 138-b. These terms apply to the bear¬ 
ing at the bottom of the column as well as 
to the loading at the top, but usually the 
bearing at the bottom is made uniform, i. e., 
concentric. 

Concentric Loads. Concentric loads, 
Fig. 139, produce direct or axial compres¬ 
sion in the column. This compression may 
be considered as evenly distributed over the 
entire cross section, even if the loads be 
balanced loads connected to opposite sides 
of the column. Then the unit stress P on 
the column is the load W divided by the area 
A : which is expressed bv the formula 

pJ j 



(o) (6) 

Fig. 138. Diagram Showing 
Examples of (a) Concentric 
Loads and (b) Eccentric 
Loads 


Conversely the capacity of a column or its total permis¬ 
sible load is the allowable unit stress multiplied by the 


area: 


W=P A 


For example, assume the load on a column to be 
190,000 pounds and the area of the assumed column 16.4 
square inches. Then the unit stress, or average compres- 
190,000 


sion, is 


or 11.585 pounds per square inch. 


16.4 

Eccentric Loads. Eccentric loads, Fig. 140, produce 
axial compression and in addition cause bending stresses. 

The axial compression is determined in the same way 
as for concentric loads, and the bending stresses in the 
same manner as for beams, p. 81. gramofStres- 

. .. . ses from Con- 

1 he bending, or eccentric, moment of the load is the centric Loada 
amount of the load multiplied by its distance from the neutral axis of 









STEEL CONSTRUCTION 


175 


the column. The sum of the axial compression per square inch and 
the maximum compression fiber stress per square inch is the maxi¬ 
mum combined stress resulting from the eccentric load. (See Flex¬ 
ure and Compression for Beams, in “Strength of Materials”, Part 
II.) This is illustrated in Fig. 140. W' is an eccentric load. The 
direct stress in the column is represented by the area abed and 

equals W'. (This area may represent the total 
load on the column if there are other loads than 
W f .) The bending moment produces the com- 


jsLi 

H 




»V* 


7 


hPL, 

4 L* 6 Xjf><f pression obb' and the tension o c c'. Then the 
maximum fiber stress in the column is a b', being 
the sum of a 6 and b b'. On the side opposite to 
the eccentric load, the tension due to bending 
overcomes part or all of the compression due to 
direct stress. The result in this case is d c'; but 
the stress in this side of the column rarely needs 
consideration. Of course, the eccentricity may 
be so great that the opposite side of the column 
is in tension, but even this does not require 
attention unless the column is spliced. 

The total stress produced by all the loads 
equals the sum of the stresses produced by the 
loads separately*. Some authorities allow three- 
fourths of the bending moment to be used in 
computing the effect on the column. This prac¬ 
tice is satisfactory and is followed in the illus¬ 
tration used later in this book. 

Fig. 140 . Diagram of Typical Cases. The entire load on the col- 
fS^nCo^ipresmon 0 umn, including its own weight and the weight 
of the fireproofing, must be determined (making 
no distinction between concentric and eccentric loads). Then 
compute the bending moments due to the eccentric loads, 
dividing these moments between the respective axes of the 
column. 

(a) As an example, refer to Figs. 139 and 140, letting them 
represent the same column. Assume W a concentric load of 100,000 



b‘ 


•This statement is not eTactly correct but represents usual practice. 























176 


STEEL CONSTRUCTION 


pounds; W' an eccentric load of 50,000 pounds; and e an eccett 
tricity, or lever arm of W', of 10 inches. Then 


Total load = 100,000+50,000 = 150,000# 
The bending moment due to the eccentric load is 


M = 50,000X10 = 500,000 in.-lb. 


As a trial section, take a column made of 1 PI. 12"X|" and 
4Ls 6"X3^"Xf" from which c, the distance from the neutral axis to 
the extreme fiber, is 6.125 inches; r, the radius of gyration about 


the same axis as the bending moment, is 5.00 inches; the section 

c 

modulus, is 74.7 inches 3 ; and A, the area, is 18.2 square inches. 
The average stress resulting from the total load is 


150,000 

18.2 


= S240# per sq. in. 


i 


This is represented by a b in Fig. 140. 

The maximum fiber stress resulting from the bending moment, 
taking three-fourths of the computed moment, is 

1X500,000 


74.7 


= 5020# per sq. in. 


This is represented in Fig. 140 by b b' and c c' in compression and 
tension, respectively. 

Then the total maximum fiber stress in the column is 
8240+5020 = 13,260# per sq. in. 


This is represented by a b'. 

The method of determining the allowable stress has not yet 
been given so it cannot be decided whether the trial section given 
above is satisfactory. 

(b) Fig. 141 illustrates cases of concentric and eccentric load¬ 
ing. In each of them there may be a concentric load from the 
column section above. In Fig. 141-a, the loads are concentric, pro¬ 
vided those on opposite sides are equal and balance each other. 
If m be omitted, o becomes eccentric, but as it connects to the web 
of the column the eccentricity is small and usually is neglected. 
If n be omitted, p becomes eccentric with a moment arm e and a 
bending moment pXe. If n is less than p, the difference is the 
eccentric load and the bending moment is ( p—n)Xe . In Fig. 141-b, 
the load u is eccentrie about the axis 2-2, and the bending moment 




STEEL CONSTRUCTION 


177 


is uXe 2 . The resulting fiber stress must be computed from the 
moment of inertia about the same axis. The load v is eccentric 


about the axis 1 -1, and the bend 
ing moment is vXe v The result¬ 
ing fiber stress must be com¬ 
puted from the moment of inertia 
about the same axis. Both 
eccentric loads produce compres¬ 
sion at the corner d, hence the 
effects of both must be added to 
the axial stress produced by the 
total load, in order to determine 
the maximum fiber stress in the 
column. 

As an example, take Fig. 
141-b and assume the following 
data, taking for the trial section, 
a column made of 1 PI. 12" Xf" 
and 4 Ls 6"X3^"X|" from which 
/j is 213; I 2 is 721; c, is 6§"; c 2 is 
6g"; e x is 7"; e 2 is 9|"; and A is 2 



<? 


— 





J 



i! 

:i 

/ * 




r 

b ■■ 

•1 

n 

it 

!i 

n 

•i 

ii 

—HI 

II 

II 

u 

(b) 

, e\ 


2 


Fig. 141. Diagrams Showing (a) Concentric 
Load and (b) Eccentric Loads on Columns 


.7 sq. in. 


Concentric load from column section above = 150,000 

v= 30,000 
u= 45,000 

Total load =225,000# 


Unit stress from total load 


225,000 

29.7 


= 7575# per sq. in. 


M t = 30,000X7 = 210,000 in.-lb. 
f of this = 157,500 in.-lb. 


Unit fiber stress due to v — 


157,500X6| 


213 


= 4720# per sq. in. 


M 2 = 45,000X9| = 416,000 in.-lb. 
| of this = 312,000 in.-lb. 


Unit fiber stress due tow 


312,000X6| 

721 


= 2650# per sq. in. 


Total fiber stress at d = 7575+4720+2650 = 14,945# per sq. in. 












































178 


STEEL CONSTRUCTION 


Problem 

Assume a heavier column section for the example given above and compute 
the total maximum fiber stress. 

Eccentric Load In Terms of Equivalent Concentric Load. The 
effect of the eccentricity of the load can be expressed in terms of an 
equivalent concentric load, which can be added to the actual load 
and the resulting total be applied as a concentric load, giving 
the same maximum stress as if computed by means of the bending 
moment. The proportion to be added, if the full eccentricity is 
used, is given by the expression 


WJ = W' 


e c 


Or, if the reduction in eccentricity is made in accordance with the 
rule on p. 175, the expression is 



e c 


In these formulas W is the eccentric load and W e ' is the 
equivalent concentric load. Before this method can be applied, it 
is necessary to select the trial column section, and from it compute 
the values of c and r. As the values of c and r for the trial section 
will vary but little from those for the final section, it usually will be 
unnecessary to correct the equivalent concentric load computed by 
this method. 

Referring now to the example illustrated in Figs. 139 and 140 
and explained on p. 176, the eccentric effect is 

We = IX 50,000 X = 91,875 # 

5X5 

Then the total equivalent concentric load on the column is 

W = 100,000 
W'= 50,000 
W/= 91,875 


241,875# 

and the resulting stress in the column is 

^^ = 13,285# per sq. in. 

This result agrees closely with the results obtained by Use of the 
bending moment. It would agree exactly if all the computations 





STEEL CONSTRUCTION 


179 


and the values of the properties were given in more exact figures. 
Note that the equivalent concentric load is not- carried down into 
the next lower Section of column but disappears at the bottom of 
column section under consideration. 

Problem 

Compute the equivalent concentric load and the resulting unit stress for 
the eccentric loads u and v in Fig. 141-b from the data given on p. 177. 

Strength of Columns. The ideal column is perfectly straight, 
symmetrical, and homogeneous, but these conditions are never fully 
attained. The material may not be exactly straight, then inaccur¬ 
ate workmanship, the punching of rivet holes, driving of rivets, 
abuse in handling, and internal defects of the steel, all co-operate 
to produce results somewhat short of ideal. These imperfections 
are of more importance with long than with short columns, and like¬ 
wise with small columns than with large ones. 

The foregoing conditions make it necessary to use lower stresses 
in columns than are used for beams; also to vary the stresses accord¬ 
ing to the length and size ct the column. The relations cannot be 
expressed in a rational formula, that is, a formula deduced from 
theory, as is the case with beams; hence empirical formulas are 
used, i. e., formulas based on experimental data. A large number 
of tests have been made to determine the effect of the length and 
size on the strength of columns. Several formulas have been 
derived giving results agreeing closely with the tests. 

Formula for Unit Stress. The simplest of these formulas and 
the one now most generally used is 

P = 16,000-70 - 

r 

in which P is the permissible compression per square inch of cross 
section; l is.the unsupported length of column in inches; and r is the 
least radius of gyration in inches. The radius of gyration rather 
than the side or the diameter is used as the measure of the size of 
the column as it relates more directly to the stiffness. 

From the above formula the allowable stress per square inch 
can be determined for any column having known values of l and r. 
Thus if/ = 180" and r = 2.4" 

1 SO 

P = 16,000 - 70 fj = 16,000 - 5250 = 10,750 # per sq. in. 



180 


STEEL CONSTRUCTION 


Then the total capacity W equals PxA (p.174); and assuming 
A = 12.0 sq. in. 

IV= 10,750X12.0 = 129,000# 


The end condition of the column lias some effect on the strength. 
A column which has ends resting on pins or pivots will not support 
as great a load as one which has flat or fixed bearings. The formula 
given above applies to columns with flat or fixed ends and as these 
are used almost universally in building construction, the other 
formulas need not be considered in this text. Pivoted and pin ends 
for columns occur in bridge construction and the necessary formulas 
for them are given in books on that subject. 

The values given by the formula do not apply to very long or 
very short columns. The maximum value of P allowed (see Unit 
Stresses, p. 51) is 14,000 pounds. This corresponds to a value of 

— = 30, so 14,000 must be used when — is equal to, or less than, 30. 
r r 


In the other direction the limiting value of — is 120, according to most 

r 

specifications. However, larger values may be used with safety if 
particular care is taken to avoid eccentricity. 

Schneider’s Specifications provide that “No compression member 
shall have a length exceeding 125 times its least radius of gyration, 
except those for wind and lateral bracing, which may have a length 
not exceeding 150 times the least radius of gyration.”* 

The formula takes into account only the average imperfections 
in columns, and makes no allowance for the different stvles of 
columns. Nevertheless, It is known that columns with .solid web 
plates are more efficient than laced columns, and laced columns in 
turn are more efficient than columns with batten plates. There 
is no well-established practice in reference to this but a rea¬ 
sonable allowance is to deduct from the values given by the 
formula 25 per cent for laced columns and 50 per cent for battened 
columns. 

Having adopted a formula by which the allowable unit stress 
can be computed, the- example given on p. 176 can be completed. 


*Transactions American Society Civil Engineers, Vol. LIV, p. 495. ■ 



STEEL CONSTRUCTION 


181 


The trial section there used was a column made of 1 PI. 12" Xf" and 

4 Ls 6"X3§"Xi", from which r (least value) is 2.56"; and A is 18.2 
sq. in. 

Assume 1= 102". The allowable unit stress is 

P = 16,000 — 70 = 16,000 — 70 -^~ = 13,200# per sq. in. 

The maximum fiber stress computed from the assumed loading is 
13,260 pounds per square inch,, hence the trial section is satis¬ 
factory. 

Taking the example on p. 177, the trial section of column is 
made of 1 PI. 12"Xf" and 4 Ls 6"X3|"X|", from which r (least value) 
is 2.68"; and A is 29.7 sq. in. 

Assume 1= 138". -The allowable unit stress is 

P =16,000 — 70 -^^- = 12,400# per sq. in. 

2.Do 

The maximum fiber stress computed from the assumed loading is 
14.945 pounds per square inch, hence the trial section is not large 
enough and a heavier section must be tried. 

Properties of Column Sections. In the foregoing discussion of 
the formulas, it appears that certain properties of the column must 
be known before the formula can be applied. The formula for 
allowable unit stress requires the radius of gyration r and the 
unsupported length l of the column section. If the column sup¬ 
ports an eccentric load, the moment of inertia 7, or the radius 
of gyration r, and the distance to the extreme fiber c must also 
be known in order to compute the maximum fiber stress due to 
bending. 

Area. The area A is computed by adding together the areas 
of the several pieces which make up the column section. The areas 
of the individual pieces are given in the handbooks. No deduction 
is made for rivet holes. 

Distance from Neutral Axis to Extreme Fiber. The distance to 
the extreme fiber from the neutral axis is readily computed from the 
dimensions of the column section. It must be taken from the axis 1 
about which the bending moment is computed. Thus, in Fig. 


182 


STEEL CONSTRUCTION 


141-b, c 2 must be used in connection with the load u, and c, in con¬ 
nection with the load v. 

Moment of Inertia. The moment of inertia is computed by the 
method explained and illustrated on p. 37. It also must be taken 
in reference to the neutral axis about which the bending moment is 
computed. Thus in Fig. 141-b, I must be calculated in reference to 
axis 2-2 for the load it, and to axis 1-1 for the load v. 

Radius of Gyration. The radius of gyration is computed about 
each axis by the method explained and illustrated on p. 38. The 
lesser value is usually required for computing the unit stress, but 
either or both may be required for computing eccentric effects. 
Thus, in Fig. 141-b, both radii of gyration are used. 

There are conditions under which the larger radius of gyration 
is used. One such case is that of a column built into a masonry 
wall in such a way that it is supported by the masonry in its weaker 
direction, Fig. 142. Then the larger radius is used, but designers 
are cautioned against using this unless the wall is so substantial that 

it gives real support to the col¬ 
umn. A casing of brick or con¬ 
crete or a poorly built brick wall 
is not sufficient. 

It sometimes happens that 
a column is supported in one 
Fig. 142. Section showing Column Supported direction at closer intervals than 

by Masonry in Its Weaker Direction . 

in the other direction. The 
weaker way of the column should be turned, if practicable, in the 
direction of the closer supports. Then the design may be governed 
by the lesser radius combined with the shorter length; or by the 
greater radius combined with the longer length. 

Unsupported Length. The length l is needed for solving the 
allowable unit stress. It is expressed in inches and is the unsup¬ 
ported length of column. This unsupported length is usually 
measured from floor to floor, but if there are deep girders with rigid 
connections, the clear distance between girders may be taken as the 
length. 

Problem 

Compute the values of A, /„ / 2 , c„ c 2 , r„ and r 2 for the column sections, 
which are shown in Fig. 143. 

















STEEL CONSTRUCTION 


183 


Column Sections. Practically all rolled sections of steel may 
be used as columns or struts, but only a few of them are economical 
when used alone. Most columns are built up of several pieces. 
Fig. 144 shows a number of sections. 

Section a. The single angle is not economical but may be used 
for a light load. When used, its radius of gyration must be taken 
about the diagonal axis. 

Section b. Two angles make a satisfactory strut for short 
lengths and light loads. Usually angles with unequal legs are used, 
with the long legs parallel. The radii about both axes are nearly 
the same for most sizes. The value about the axis 2-2 can be 
varied somewhat by the use of fillers between the angles. Such 
fillers should be spaced two to three feet apart. 



Section c. The star strut is made of two angles with batten 
plates. The batten plates in each direction are spaced from two to 
four feet apart. They must be wide enough for two rivets in each 
end. The least radius is about the diagonal axis 3-3. In accord¬ 
ance with the rule, p. 180, this being a battened section, the unit 
stress should be only one-half that given by the formula. Conse¬ 
quently, the section is not economical but is suitable to use when 
the load is light. It is quite useful as a brace between trusses and 
other similar situations. 

Section d. Four angles placed at the corners of a square and 
joined together with lacing bars can be made to have a large radius 
of gyration with a small area. This makes a column suitable for 
supporting light loads on . a long length. It is not suitable for 
eccentric loads. The spacing of the angles may be made as great 














































( 5 ) 

2 





/ 

/ 

^ WTO < 



z 







Fig. 144. Typical Column Sections 



(v) 






•(</) 

















































































































































































STEEL CONSTRUCTION 


185 


as required by the conditions. The allowable unit stress on this 
section must be reduced on account of the lacing in accordance with 
the rule, p. 180. However, if the column is filled and encased in 
concrete, the full unit stress may be used. It is well adapted to 
use in this way. On account of the weight of the lacing and the 
cost of shop labor, this section is more expensive than most others 
for a given area, hence it is used only for conditions described 
above. 

Sectio?i e. When the angles are placed in this form, the cost of 
shop work is somewhat reduced, but otherwise the above comments 
apply. 

Section f. The Gray column* is made of eight angles joined 
together in pairs and these pairs are assembled into a column by 
means of batten or tie plates. The batten plates are usually made 
8" X f" and spaced 2'-6", center to center The advantages of this sec¬ 
tion are its large radius of gyration and ease of making connections 
for beams and girders. Its disadvantages are that it is a battened 
column and, therefore, not capable of carrying the full unit stress 
given by the column formula; and that the expense of its manufacture 
is high, due to the bent batten plates. It has been used extensively 
with the full unit stress; however, it seems more reasonable to make 
some reduction. Since the battens are quite rigid the column is 
probably as good as a laced column, hence it can be used with a 
reduction of 25 per cent from the full unit stress. This column is not 
adapted to eccentric loads and is best suited to load conditions 
which would bring in equal loads to each of its four parts. This 
seldom occurs, the most common arrangement being two girders on 
opposite sides and two joists on the other sides. Thus two 
segments of the column are loaded much more heavily than the 
other two. The batten plates cannot be relied upon to equalize 
the load, but heavier angles can be used for the heavier loads. If 
this system of proportioning each segment to suit the loads which 
connect directly to it is used, the chief objection to this type of 
column is eliminated. 

When filled and encased in concrete, the Gray column is very 
rigid and can then be loaded to the full unit stress. It is especially 
suitable as the core of concrete columns, and can be used thus in 


•Designed and patented by J. H. Gray, C.E., New York, N. Y. 



186 


STEEL CONSTRUCTION 


connection with reinforced concrete floor framing. When so used, 
the column may be rotated 45 degrees from the axis of the girders 
if it is desired to pass the reinforcing rods through the column. 
The bearing of the beams and girders in part can be directly on the 
concrete core and in part on lug angles riveted to the faces of the 
column. 

The Gray column can be made any desired size using any 
standard angles. The practicable limits are ten inches square 
(minimum) and twenty inches square (maximum). 

Section g. A column made of jour angles laced has little merit as 
compared with the plate and angle column which is next described. 
Its only claim is that in some cases it may. be cheaper to use lacing 
than to use a web plate. This would be so if there were some 
special condition requiring a deep column. As with other laced 
columns, it should not be allowed the full unit stress and should not 
be subject to any considerable eccentricity. 

Section h. The plate and angle column is probably the most pop¬ 
ular shape for buildings. It does not give the most economical dis¬ 
tribution of metal, as the value of r is much greater about the axis 1-1 
than about 2-2. Its advantages are economy of manufacture and 
ease of making connections. Advantage can be taken of the greater 
value of r (and therefore of 7) about the axis 1-1, in providing for 
eccentric loads by so placing the column that'the bending moment 
is about this axis. 

Sections i, j, and k. In the use of heavy forms of plate and angle 
columns, a considerable variation in area can be made by varying 
the thickness of metal, keeping the depth constant, and making only 
a slight change in the width. If greater area is needed, flange and 
web plates may be added as in i, and still greater area may be 
secured by using the forms j and k. Section k is difficult to fabricate. 
The flange plates must be riveted to the center web first, and after 
this is done it is difficult to insert the outside web. 

Section l. Two channels laced have a large value of r in propor¬ 
tion to the area. The channels can be so spaced that the values of 
r for both axes are about equal. This section of column has the 
same disadvantages as to unit stress and eccentric loads as other 
laced columns. The connections for beams and columns are more 
difficult to make than on plate and angle columns. 


STEEL CONSTRUCTION 


187 


Sections m, n, and o. The columns made of channels and plates 
have good distribution of metal. Their chief disadvantage is the 
difficulty of making connections. All rivets in connections, except 
those which go through the flanges of the channels, must be driven 
before the plates and channels are assembled. The section o, having 
three webs, has the same difficulty of fabrication as section k. Ob¬ 
jection is sometimes made to the closed box section. This is dis¬ 
cussed later. 

Sections p. and q. Section p is the standard Z-bar column, and 
section q is the Z-bar column with flange plates. The distribution 
of metal is not as good as in channel columns and the connections 
are even more difficult. These sections were formerly much used 
but now only rarely. 

Section r. The standard I-beam is not an economical column 
section but is used to meet special conditions. It is suitable when 
built into a solid masonry wall with its web perpendicular to the 
axis of the wall. It is thus supported sidewise continuously and 
can be designed in reference to its larger radius of gyration. In 
apartment or residence work it is sometimes so desirable to keep 
the column within the thickness of the partition that the lack of 
economy of the I-beam column is justified. 

Sections s, t, u, and v. The columns s, t, u, and v are not much 
used. There are no serious objections to any of them, and they may 
have advantages in special situations. Quick service from stock 
material may require the use of these sections. 

Section w. The Carnegie H -sections are designed especially for 
use as columns. There are only four sizes, viz, 4, 5, 6, and 8 inches, 
respectively, and only one weight for each size, consequently their 
range of usefulness is very limited. The radius of gyration about 
the axis 1-1 is greater than that about 2-2, but the distribution of 
metal is as good as in any H-shaped column. They are economical 
because so little labor is required for fabricating them. Only the 
6-inch and 8-inch sizes can be used where beams must be connected 
to the flanges. 

Sections x and y. The Bethlehem columns have a large range of 
sizes and weights. If the H-section in x is not heavy enough for the 
load, it can be increased by riveting on flange plates as in y. The 
advantage of this type of column is economy of fabrication, the only 


188 


STEEL CONSTRUCTION 


riveting required being for connections, except when flange plates 
are used. A part of this advantage is lost in the heavier sections 
because all holes must be drilled, due to thickness of metal. The 
thick metal is not as strong nor as reliable as the thinner metal used 
in built-up sections. 

Tables. No comprehensive set of tables giving the properties 
and strength of columns has been published. But there are many 
partial tables which are of great assistance in designing. These 
tables can be divided into three classes as follows: (1) tables giving 
the properties of the sections; (2) tables giving the values of the 

allowable unit stresses for different values of —; and (3) tables giving 

r 

strength of columns of various sections and lengths. 

Properties of Sections. The properties of sections needed are 
area A; radius of gyration r; moment of inertia /; and distance to 
extreme fiber c. (See p. 181). If the column is a single rolled 
section, its properties can be taken from the tables in the handbooks. 
The values for standard angles and I-beams are given in all the 
handbooks; for the. Carnegie H-columns, in the Carnegie Pocket 
Companion, 1913 edition; and for the Bethlehem columns, in the 
Bethlehem handbook. 

Built-up columns may be made up in such vast numbers of 
combinations that no complete or very extensive tables have been 
published. However, the more common sizes are given in some of 
the handbooks. The area A and the distance to the extreme fiber 
c are readily computed from the sizes of material used in the column. 
The Cambria and Carnegie (1913) handbooks give the radii of 
gyration r and the moments of inertia / for laced channel columns, 
plate and channel columns, and plate and angle columns. The 
Carnegie handbook (1903) gives these properties for Z-bar columns. 
Similar data for about the same range of sizes are given in a number 
of other books on steel construction. 

Allowable Unit Stress. The allowable unit stress adopted for 
this work has been given and illustrated heretofore. Its formula is 

P= 16,000-70- 

r 

This is sometimes known as the American Railway Engineers’ 
formula and is hereinafter referred to as the A. R. E. formula. 


STEEL CONSTRUCTION 


189 


In the Carnegie Pocket Companion, (1913 Edition) pp. 254-5. 
are shown a table and a diagram which give the values of P as 
determined from several other formulas. The formula recom¬ 
mended by the American Bridge Company does not differ greatly 
from the A. R. E. formula and may be used (unless local building 
ordinances require otherwise). 

The formula used by the Bethlehem Steel Company is 

P = 16,000-55- 
r 

with a maximum value 13,000. The resulting unit stresses for 

values of — greater than 45 are higher than given by the A. R. E. 
r 

formula, and for values of - greater than 65 are higher than given by 

r 

V 

the American Bridge Company formula. 

It saves much time in designing to have the values of P worked 
out for the usual values of l and r. Table V gives the values of P 
for values of r ranging from 0.1 inch to 6.0 inches and for lengths 
ranging from 3 feet to 40 feet. Table VI gives the values of P for 

values of — ranging from 30 to 150. 
r 

Strength of Columns. As indicated above, there has not been 
general agreement on the formula for the allowable unit stress, 
consequently the tables of strength of columns-which have been 
published have been based on several different formulas. 

The Bethlehem handbook gives the strength of Bethlehem H- 
columns computed from their formula given above. Table VII 
gives the strengths of these columns based on the A. R. E. formula. 
(Computed by the Bethlehem Steel Company, for use in Chicago.) 

The Carnegie Pocket Companion (1913) gives tables for Car¬ 
negie H-columns, I-beam columns, channel columns, and plate and 
angle columns, based on the American Bridge Company formula. 

Table VIII gives the strengths of channel columns based on 
the A. R. E. formula (computed by the American Bridge Company). 
The strengths of plate and angle columns based on the A. R. E. 
formula are given in a pamphlet “Specifications for Steel Structures” 
(Chicago Edition), published by the American Bridge Company 
and distributed by its Chicago office. 


190 


STEEL CONSTRUCTION 


TABLE V 

Unit Stress in Compression in Columns 

For values of r from 0.1 to 6.0 and lengths from 3 feet to 40 feet . Unit Stresses 
are given in Thousands of Pounds per Square Inch . 

Radius of 
Gyration 

LENGTH OF COLUMN 

3' 

4' 

5' 

6' 

T 

8' 

9' 

10' 

11' 

12' 

13' 

14' 

15' 

16' 

0.1 















0.2 















0.3 

7.6 














0.4 

9.7 

7.6 

5.5 












0.5 

11.0 

9.3 

7.6 

5.9 











0.6 

11.8 

10.4 

9.0 

7.6 

6.2 










0.7 

12.4 

11.2 

10.0 

8.8 

7.6 

6.4 









0.8 

12.8 

11.8 

10.7 

9.7 

8.6 

7.6 

6.5 

5.5 







0.9 

13.2 

12.3 

11.3 

10.4 

9.5 

8.5 

7.6 

6.7 

5.7 






1.0 

13.5 

12.6 

11.8 

11.0 

10.1 

9.3 

8.4 

7.6 

6.8 

5.9 





1.1 

13.7 

12.9 

12.2 

11.4 

10.6 

9.9 

9.1 

8.4 

7.6 

6.8 

6.1 




1.2 

13.9 

13.2 

12.5 

11.8 

11.1 

10.4 

9.7 

9.0 

8.3 

7.6 

6.9 

6.2 

5.5 


1.3 

14.1 

13.4 

12.8 

12.1 

11.5 

10.8 

10.2 

9.5 

8.9 

8.2 

7.6 

6.9 

6.3 

5.7 

1.4 

14.2 

13.6 

13.0 

12.4 

11.8 

11.2 

10.6 

10.0 

9.4 

8.8 

8.2 

7.6 

7.0 

6.4 

1.5 

14.3 

13.8 

13.2 

12.6 

12.1 

11.5 

11.0 

10.4 

9.8 

9.3 

8.7 

8.2 

7.6 

7.0 

1.6 

14.4 

13*9 

13.4 

12.8 

12.3 

11.8 

11.3 

10.7 

10.2 

9.7 

9.2 

8.6 

8.1 

7.6 

1.7 

14.5 

14.0 

13.5 

13.0 

12.5 

12.0 

11.5 

11.1 

10.6 

10.1 

9.6 

9.1 

8.6 

8.1 

1.8 

14.6 

14.1 

13.7 

13.2 

12.7 

12.3 

11.8 

11.3 

10.9 

10.4 

9.9 

9.5 

9.0 

8.5 

1.9 

14.7 

14.2 

13.8 

13.3 

12.9 

12.5 

12.0 

11.6 

11.1 

10.7 

10.2 

9.8 

9.4 

8.9 

2.0 

14.7 

14.3 

13.9 

13.5 

13.1 

12.6 

12.2 

11.8 

11.4 

11.0 

10.5 

10.1 

9.7 

9.3 

2.1 

14.8 

14.4 

14.0 

13.6 

13.2 

12.8 

12.4 

12.0 

11.6 

11.2 

10.8 

10.4 

10.0 

9.6 

2.2 

14.8 

14.5 

14.1 

13.7 

13.3 

12.9 

12.0 

12.2 

11.8 

11.4 

11.0 

10.6 

10.3 

9.9 

2.3 

14.9 

14.5 

14.2 

13.8 

13.4 

13.1 

12.7 

12.3 

12.0 

11.6 

11.2 

10.9 

10.5 

10.2 

2.4 

14.9 

14.6 

14.2 

13.9 

13.5 

13.2 

12.8 

12.5 

12.1 

11.8 

11.4 

11.1 

10.7 

10.4 

2.5 

15.0 

14.7 

14.3 

14.0 

13.6 

13.3 

13.0 

12.6 

12.3 

12.0 

11.6 

11.3 

11.0 

10.6 

2.6 

15.0 

14.7 

14.4 

14.1 

13.7 

13.4 

13.1 

12.8 

12.4 

12.1 

11.8 

11.5 

11.1 

10.8 

2.7 

15.1 

14.8 

14.4 

14.1 

13.8 

13.5 

13.2 

12.9 

12.6 

12.3 

12.0 

11.6 

11.3 

11.0 

2.8 

15.1 

14.8 

14.5 

14.2 

13.9 

13.6 

13.3 

13.0 

12.7 

12.4 

12.1 

11.8 

11.5 

11.2 

2.9 

15.1 

14.8 

14.5 

14.3 

14.0 

13.7 

13.4 

13.1 

12.8 

12.5 

12.2 

11.9 

11.7 

11.4 

3.0 

15.2 

14.9 

14.6 

14.3 

14.0 

13.8 

13.5 

13.2 

12.9 

12.6 

12.4 

12.1 

11.8 

11 . 5 1 

Radius of 
Gyration 

3' 

4' 

5' 

6' 

r 

8' 

9' 

10' 

ir 

12' 

13' 

14' 

15' 

16' 








































































STEEL CONSTRUCTION 


191 


TABLE V (Continued) 

l 

Formula P = 16,000 - 70 ~ 

in which P =unit stress in pounds per square inch 

r — radius of gyration in inches 

X —length in inches 

l 

Unit stresses above the heavy zigzag line are values of — from 125 to 150 

LENGTH OF COLUMN 

Radius of 

Gyration 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 25' 

26' 

27' 

28' 29' 

30' 















0.1 















0.2 















0.3 















0.4 















0.5 















0.6 















0.7 















0.8 















0.9 















1.0 















1.1 















1.2 















1.3 

5.8 














1.4 

65 

5.9 













1.5 

7.1 

6.5 

6.0 

5.5 











1.6 

7.6 

7.1 

6.6 

6.1 

5.6 










1.7 

8.1 

7.6 

7.1 

6.7 

6.2 

5.7 









1.8 

' 8.5 

8.0 

7.6 

7.2 

6.7 

6.3 

5.8 








1.9 

8.9 

8.4 

8.0 

7.6 

7.2 

6.8 

6.3 

5.9 

5.5 






2.0 

9.2 

8.8 

8.4 

8.0 

7.6 

7.2 

6.8 

6.4 

6.0 

5.6 





2.1 

9.5 

9.1 

8.7 

8.4 

8.0 

7.6 

7.2 

6.8 

6.4 

6.1 

5.7 




2.2 

9.8 

9.4 

9.1 

8.7 

8.3 

8.0 

7.6 

7.2 

6.9 

6.5 

6.1 

5.8 



2.3 

10.0 

9.7 

9.3 

9.0 

8.6 

8.3 

7.9 

7.6 

7.2 1 

6.9 

6.5 

6.2 

5.8 

5.5 

2.4 

10.3 

9.9 

9.6 

9.3 

8.9 

8.6 

8.3 

7.9 

7.6 

7.3 

6.9 

6.6 

6.3 

5.9 

2.5 

10.5 

10.2 

9.9 

9.5 

9.2 

8.9 

8.6 

8.2 

7.9 

7.6 

7.3 

6.9 

6.6 

6.3 

2.6 

10.7 

10.4 

10.1 

9.8 

9.5 

9.2 

8.8 

8.5 

8.2 

7.9 

7.6 

7.3 

7.0 

6.7 

2.7 

10.9 

10.6 

10.3 

10.0 

9.7 

9.4 

9.1 

8.8 

8.5 

8.2 

7.9 

7.6 

Ts] 

7.0 

2.8 

11.1 

10.8 

10.5 

10.2 

9.9 

9.6 

9.3 

9.0 

8.8 

8.5 

8.2 

7.9 

7.6 

7.3 

2.9 

11.2 

11.0 

10.7 

10.4 

10.1 

9.8 

9.6 

9.3 

9.0 

8.7 

8.4 

8.2 

7.9 

7.6 

3.0 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

25' 

26' 

27' 

00 

CM 

29' 

30' 

Radius of 
Gyration 




























































192 


STEEL CONSTRUCTION 


TABLE V (Continued) 

Unit Stress in Compression in Columns 


For values of r from 0.1 to 6.0 and lengths from 3 feet to 40 feet. Unit Stresses 
are given in Thousands of Pounds per Square Inch 


Radius of 
Gyration 

LENGTH OF COLUMN 

8' 

9' 

10' 

11' 

12' 

13' 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

3.1 

13.8 

13.6 

13.3 

13.0 

12.7 

12.5 

12.2 

11.9 

11.7 

11.4 

11.1 

10.8 

10.6 

10.3 

3.2 

13.9 

13.6 

13.4 

13.1 

12.8 

12.6 

12.3 

12.1 

11.8 

11.5 

11.3 

11.0 

10.7 

10.5 

3.3 

14.0 

13.7 

13.4 

13.2 

12.9 

12.7 

12.4 

12.2 

11.9 

11.7 

11.4 

11.2 

10.9 

10.6 

3.4 

14.0 

13.8 

13.5 

13.3 

13.0 

12.8 

12.5 

12.3 

12.0 

11.8 

11.5 

11.3 

11.1 

10.8 

3.5 

14.1 

13.8 

13.6 

13.4 

13.1 

12.9 

12.6 

12.4 

12.2 

11.9 

11.7 

11.4 

11.2 

11.0 

3.6 

14.1 

13.9 

13.7 

13.4 

13.2 

13.0 

12.7 

12.5 

12.3 

12.0 

11.8 

11.6 

11.3 

11.1 

3.7 

14.2 

14.0 

13.7 

13.5 

13.3 

13.0 

12.8 

12.6 

12.4 

12.1 

11.9 

11.7 

11.5 

11.2 

3.8 

14.2 

14.0 

13.8 

13.6 

13.3 

13.1 

12.9 

12.7 

12.5 

12.2 

12.0 

11.8 

11.6 

11.4 

3.9 

14.3 

14.1 

13.8 

13.6 

13.4 

13.2 

13.0 

12.8 

12.5 

12.3 

12.1 

11.9 

11.7 

11.5 

4.0 

14.3 

14.1 

13.-9 

13.7 

13.5 

13.3 

13.1 

12.8 

12.6 

12.4 

12.2 

12.0 

11.8 

11.6 

4.1 

14.4 

14.2 

13.9 

13.7 

13.5 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.1 

11.9 

11.7 

4.2 

14.4 

14.2 

14.0 

13.8 

13.6 

13.4 

13.2 

13.0 

12.8 

12.6 

12.4 

12.2 

12.0 

11.8 

4.3 

14.4 

14.2 

14.0 

13.8 

13.6 

13.5 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.1 

11.9 

4.4 

14.5 

14.3 

14.1 

13.9 

13.7 

13.5 

13.3 

13.1 

12.9 

12.8 

12.6 

12.4 

12.2 

12.0 

4.5 

14.5 

14.3 

14.1 

13.9 

13.8 

13.6 

13.4 

13.2 

13.0 

12.8 

12.6 

12.4 

12.3 

12.1 

4.6 

14.5 

14.4 

14.2 

14.0 

13.8 

13.6 

13.4 

13.3 

13.1 

12.9 

12.7 

12.5 

12.3 

12.2 

4.7 

14.6 

14.4 

14.2 

14.0 

13.8 

13.7 

13.5 

13.3 

13.1 

13.0 

12.8 

12.6 

12.4 

12.2 

4.8 

14.6 

14.4 

14.2 

14.1 

13.9 

13.7 

13.5 

13.4 

13.2 

13.0 

12.8 

12.7 

12.5 

12.3 

4.9 

14.6 

14.5 

14.3 

14.1 

13.9 

13.8 

13.6 

13.4 

13.3 

13.1 

12.9 

12.7 

12.6 

12.4 

5.0 

14.7 

14.5 

14.3 

14.1 

14.0 

13.8 

13.6 

13.5 

13.3 

13.1 

13.0 

12.8 

12.6 

12.5 

5.1 

14.7 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.5 

13.4 

13.2 

13.0 

12.9 

12.7 

12.5 

5.2 

14.7 

14.5 

14.4 

14.2 

14.1 

13.9 

13.7 

13.6 

13.4 

13.2 

13.1 

12.9 

12.8 

12.6 

5.3 

14.7 

14.6 

14.4 

14.3 

14.1 

13.9 

13.8 

13.6 

13.5 

13.3 

13.1 

13.0 

12.8 

12.7 

5.4 

14.7 

14.6 

14.4 

14.3 

14.1 

14.0 

13.8 

13.7 

13.5 

13.3 

13.2 

13.0 

12.9 

12.7 

5.5 

14.8 

14.6 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.6 

13.4 

13.2 

13.1 

12.9 

12.8 

5.6 

14.8 

14.6 

14.5 

14.3 

14.2 

14.0 

13.9 

13.7 

13.6 

13.4 

13.3 

13.1 

13.0 

12.8 

5.7 

14.8 

14.7 

14.5 

14.4 

14.2 

14.1 

13.9 

13.8 

13.6 

13.5 

13.3 

13.2 

13.0 

12.9 

5.8 

14.8 

14.7 

14.5 

14.4 

14.3 

14.1 

14.0 

13.8 

13.7 

13.5 

13.4 

13.2 

13.1 

13.0 

5.9 

14.9 

14.7 

14.6 

14.4 

14.3 

14.1 

14.0 

13.9 

13.7 

13.6 

13.4 

13.3 

13.1 

13.0 

6.0 

14.9 

14.7 

14.6 

14.5 

14.3 

14.2 

14.0 

13.9 

13.8 

13.6 

13.5 

13.3 

13.2 

13.1 

Radius of 
Gyration 

8' 

9' 

10' 

1.1' 

12' 

13' 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 























































STEEL CONSTRUCTION 


103 


TABLE V (Continued) 

l 

Formula P= 16,000 —70 “ 

r 

in which P = unit stress in pounds per square inch 

r— radius of gyration in inches. 

1 = length in inches. 


Unit stresses above the heavy zigzag line are values of — from 125 to 150 

r 


LENGTH OF COLUMN 

o a 

C/3 .2 

22 ' 

23 ' 

24' 

25 ' 

26 ' 

27 ' 

28 ' 

29 ' 

30 ' 

32 ' 

34 ' 

36 ' 

38 ' 

40 ' 

a 

« a 

10.0 

9.8 

9.5 

9.2 

8.9 

8.7 

8.4 

8.1 

7.9 

7.3 

6.8 

6.2 

5.7 


3.1 

10.2 

10.0 

97 

9.4 

9.2 

8.9 

8.6 

8.4 

8.1 

7.6 

7.1 

6.5 

6.0 

5.5 

3,2 

10.4 

10.1 

9.9 

9.6 

9.4 

9.1 

8.9 

8.6 

8.4 

7.8 

7.3 

6.8 

6.3 

5.8 

3.3 

10.6 

10.3 

10.1 

9.8 

9.6 

9.3 

9.1 

8.8 

8.6 

8.1 

7.6 

7.1 

6.6 

6.1 

3.4 

10.7 

10.5 

10.2 

10.0 

9.8 

9.5 

9.3 

9.0 

8.8 

8.3 

7.8 

7.4 

6.9 

6.4 

3.5 

10.9 

10.6 

10.4 

10.2 

9.9 

9.7 

9.5 

9.2 

9.0 

8.5 

8.1 

7.6 

7.1 

6.7 

3.6 

11.0 

10.8 

10.5 

10.3 

10.1 

9.9 

9.6 

9 . 4 . 

9.2 

8.7 

8.3 

7.8 

7.4 

6.9 

3.7 

11.1 

10.9 

10.7 

10.5 

10.2 

10.0 

9.8 

9.6 

9.4 

8.9 

8.5 

8.0 

7.6 

7.2 

3.8 

11.3 

11.0 

10.8 

10.6 

10.4 

10.2 

10.0 

9.7 

9.5 

9.1 

8.7 

8.2 

7.8 

7.4 

3.9 

11.4 

11.2 

11.0 

10.7 

10.5 

10.3 

10.1 

9.9 

9.7 

9.3 

8.9 

8.4 

8.0 

7.6 

4.0 

11.5 

11.3 

11.1 

10.9 

10.7 

10.5 

10.3 

10.1 

9.8 

9.4 

9.0 

8.6 

8.2 

7.8 

4.1 

11.6 

11.4 

11.2 

11.0 

10.8 

10.6 

10.4 

10.2 

10.0 

9.6 

9.2 

8.8 

8.4 

8.0 

4.2 

11.7 

11.5 

11.3 

11.1 

10.9 

10.7 

10.5 

10.3 

10.1 

9.7 

9.4 

9.0 

8.6 

8.2 

4.3 

11.8 

11.6 

11.4 

11.2 

11.0 

10.8 

10.7 

10.5 

10.3 

9.9 

9.5 

9.1 

8.7 

8.4 

4.4 

11.9 

11.7 

11.5 

11.3 

11.1 

11.0 

10.8 

10.6 

10.4 

10.0 

9.6 

9.3 

8.9 

8.5 

4.5 

12.0 

11.8 

11.6 

11.4 

11.2 

11.1 

10.9 

10.7 

10.5 

10.2 

9.8 

9.4 

9.1 

8.7 

4.6 

12.1 

11.9 

11.7 

11.5 

11.3 

11.2 

11.0 

10.8 

10.6 

10.3 

9.9 

9.6 

9.2 

8.8 

4.7 

12.1 

12 0 

11.8 

11.6 

11.4 

11.3 

11.1 

10.9 

10.7 

10.4 

10.0 

9.7 

9.3 

9.0 

4.8 

12.2 

12.1 

11.9 

11.7 

11.5 

11.4 

11.2 

11.0 

10.9 

10.5 

10.2 

9.8 

9.5 

9.1 

4.9 

12.3 

12.1 

12.0 

11.8 

11.6 

11.5 

11.3 

11.1 

11.0 

10.6 

10.3 

9.9 

9.6 

9.3 

5.0 

12.4 

12.2 

120 

11.9 

11.7 

11.5 

11.4 

11.2 

11.1 

10.7 

10.4 

10.1 

9.7 

9.4 

5.1 

12.4 

12.3 

12.1 

12.0 

11.8 

11.6 

11.5 

11.3 

11.1 

10.8 

10.5 

10.2 

9.9 

9.5 

5.2 

12.5 

12.3 

12.2 

12.0 

11.9 

11.7 

11.6 

11.4 

11.2 

10.9 

10.6 

10.3 

10.0 

9.7 

5.3 

12.6 

12.4 

12.3 

12.1 

11.9 

11.8 

11.6 

11.5 

11.3 

11.0 

10.7 

10.4 

10.1 

9.8 

5.4 

12.6 

12.5 

12.3 

12.2 

12.0 

11.9 

11.7 

11.6 

11.4 

11.1 

10.8 

10.5 

10.2 

9.9 

5.5 

12.7 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.6 

11.5 

11.2 

10.9 

10.6 

10.3 

10.0 

5.6 

12.8 

12.6 

12.5 

12.3 

12.2 

12.0 

11.9 

11.7 

11.6 

11.3 

11.0 

10.7 

10.4 

10.1 

5.7 

12.8 

12.7 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.6 

11.4 

11.1 

10.8 

10.5 

10.2 

5.8 

12.9 

12.7 

12.6 

12.4 

12.3 

12.2 

12.0 

11.9 

11.7 

11.4 

11.2 

10.9 

10.6 

10.3 

5.9 

12.9 

12.8 

12.6 

12.5 

12.4 

12.2 

12.1 

11.9 

11.8 

11.5 

11.2 

11.0 

10.7 

10.4 

6.0 

22' 

23' 

rt 

CM 

25' 

26' 

F- 

CM 

28' 

29' 

30' 

32' 

CO 

-U 

36' 

CO 

CO 

40' 

Radius of 
Gyration 
























































































194 


STEEL CONSTRUCTION 


TABLE VI 


Unit Stress in Compression 


Values of P for values of — = 30 to 

r 


— =150 from the formula 
r 


P= 16,000-70 


l 

r 


1 

r 

16,000-70- 

r 

14,000 max. 

£ 

r 

16,000-70- 

r 

14,000 max. 

30 

13900 

105 

8650 

35 

13550 

110 

8300 

40 

13200 

115 

7950 

45 

12850 

120 

7600 

50 

12500 

125 

7250 

55 

12150 

130 

6900 

60 

11800 

135 

6550 

65 

11450 

140 

6200 

70 

11100 

145 

5850 

75 

10750 

150 

5500 

80 

10400 



85 

10050 



90 

9700 



95 

9350 



100 

9000 




It must be noted that the tables of strength of columns take no 
account of eccentricity. If there are eccentric loads, the equivalent 
concentric loads must be computed by the method given on p. 178, 
and then these values added to the actual loads. This result gives 
the total load to be used in selecting the column section from the 
tables. 

Use of the Tables. The following illustrations show the manner 
of using the tables: 

(1) Assume a concentric load of 492,000 pounds on a column 
12 feet long. Determine the required column sections made of plates 
and channels and of plates and angles. Compare the areas of the 
two columns. 

(a) From Table VIII, the channel column section required is 

2 E 12" X 30" 

2 PI. 14" X U" 

Area = 36.9 sq. in. 









STEEL CONSTRUCTION 


195 


(b) From the table of plate and angle columns (see handbook), 
the angle column section required is 

1 PI. 12" XV 

4 Ls 6"X4"xr 

2 PI. 14"X V 
Area = 39.0 sq. in. 

In both cases other sections might be selected. 

(2) Assume a load of 640,000 pounds on a column 16 feet long; 
80,000 pounds of the load has an eccentricity of 9 inches in the direc¬ 
tion of the greatest radius of gyration. Determine the plate and 
angle column required, using the A. R. E. formula. 

A preliminary selection from the table indicates a column whose 
greatest r is about 6.8 inches and whose c is about 8^ inches. From 
these approximate values the concentric equivalent load is 

qvKl 

W e = § x 80,000 X -4^- = 99,000 # 

6.8X6.8 

This added to the direct load gives a total of 739,000 pounds. The 
column section required is 

1 PI. 14" X |" 

4 Ls 6" X 4" X 

2 PI. 14"XI*" 

The values of r and c for this section are 6.83 inches and 8* inches, 
so the approximate values of r and c used above are accurate 
enough, hence no corrections need be made. 

(3) Assume a column which has an unsupported length of 10 
feet 6 inches in its weaker direction and 18 feet in its stronger direc¬ 
tion made of 

1 PI. 12"Xf 
4 Ls 6"X4"Xf" 

Determine the allowable unit stress. 

From the table the values of r are 2.69 and 4.91. The cor¬ 
responding values of l are 126 inches and 216 inches; and of ^ are 

43 and 44. The respective unit stresses are taken from Table VI by 
interpolating between the values for 40 and 45, giving 13,590 and 
13,720. The smaller value must be used. 



196 


STEEL CONSTRUCTION 


TABLE VII 

Safe Loads on Bethlehem Columns 
14" H-Section with Cover Plates 
Safe Loads are given in Thousands of Pounds 


Weight 

Dimensions, in. 

Area of 

Least 

UNSUPPORTED LENGTH 

Section 

Lb. 

per Ft. 

C 

P 

H 

Section 

Square 

Inches 

Radius 
of Gyr., 

Inches 

10 

11 

ir 

13 

14 

15 

284.0 

16 

IX 

16X 

83.52 

3.98 

1160.0 

1142.4 

1124.8 

1107.2 

1089.6 

1072.0 

290.8 

16 

Ire 

16% 

85.52 

3.99 

1188.2 

1170.2 

1152.2 

1134.2 

1116.2 

1098.2 

297.6 

16 

1% 

16% 

87.52 

4.01 

1217.0 

1198.6 

1180.4 

1162.0 

1143.6 

1125.4 

304.4 

16 

1A 

17 

89.52 

4.02 

1245.2 

1226.6 

1207.8 

1189.2 

1170.4 

1151.8 

311.2 

16 

l % 

17 X 

91.52 

4.04 

1274.0 

1255.0 

1236.0 

1207.0 

1198.0 

1178.8 

318.0 

16 

1^ 

17% 

93.52 

4.05 

1302.4 

1283.0 

1263.6 

1244.2 

1224.8 

1205.4 

324.8 

16 

1 % 

17% 

95.52 

4.06 

1330.6 

1311.0 

1291.2 

1271.4 

1251.6 

1231.8 

331.6 

16 

1H 

17 X 

97.52 

4.08 

1359.6 

1339.4 

1319.4 

1299.4 

1279.2 

1259.2 

338.4 

16 

w 

17 X 

99.52 

4.09 

1388.0 

1367.4 

1347.0 

1326.6 

1306.2 

1285.8 

345.2 

16 

lH 

17% 

101.52 

4.10 

1416.4 

1395.6 

1374.8 

1354.0 

1333.2 

1312.4 

350.3 

17 

IX 

17 X 

103.02 

4.30 

1447.0 

1427.0 

1406.8 

1386.6 

1366.6 

1346.4 

357.5 

17 

lH 

17% 

105.15 

4.31 

1477.4 

1457.0 

1436.4 

1416.0 

1395.4 

1375.0 

364.7 

17 

IX 

17 % 

107.27 

4.32 

1507.8 

1486.0 

1466.0 

1445.2 

1424.4 

1403.4 

372.0 

17 

ill 

1 16 

18 

109.40 

4.33 

1538.2 

1517.0 

1495.8 

1474.6 

1453.2 

1432.0 

379.2 

17 

2 

18% 

111.52 

4.35 

1569.0- 

1547.4 

1526.0 

1504.4 

1482.8 

1461.2 

386.4 

17 

21*5 

i&x 

113.65 

4.36 

1599.4 

1577.6 

1555.6 

1533.8 

1511.8 

1490.0 

393.6 

17 

2% 

18% 

115.72 

4.37 

1629.8 

1607.6 

1585.2 

1563.0 

1440.8 

1518.6 

400.9 

17 

2A 

18%2 

117.90 

4.38 

1660.2 

1637.6 

1615.0 

1592.4 

1569.8 

1547.2 

408.1 

17 

2X 

18% 

120.02 

4.39 

1690.6 

1667.8 

1644.8 

1621.8 

1598.8 

1575.8 

415.3 

17 

2A 

18% 

122.15 

4.40 

1721.2 

1697.8 

1674.6 

1651.2 

1628.0 

1604.6 

. 423.4 

18 

2 X 

18% 

124.52 

4.62 

1766.0 

1743.2 

1720.6 

1698.0 

1675.4 

1652.8 

431.0 

18 

2A 

18% 

126.77 

4.63 

1798.4 

1775.4 

1752.4 

1729.4 

1706.4 

1683.4 

438.7 

18 

2 H 

18% 

129.02 

4.64 

1830.8 

1807.4 

1784.0 

1760.6 

1737.4 

1714.0 

446.3 

18 

2ts 

19 

131.27 

4.65 

1863.2 

1839.4 

1814.8 

1792.0 

1768.4 

1744.6 

454.0 

18 

2M 

19% 

133.52 

4.66 

1895.6 

1871.6 

1847.6 

1823.4 

1799.4 

1775.4 

461.6 

18 

2A 

19% 

135.77 

4.67 

1928.2 

1903.6 

1879.2 

1854.8 

1830.4 

1806.0 

469.3 

18 

2H 

19% 

138.02 

4.68 

1960.6 

1935.8 

1911.0 

1886.2 

1861.6 

1836.8 

476.9 

18 

2U 

19% 

140.27 

4.69 

1993.0 

1968.0 

1942.8 

1917.8 

1892.6 

1867.4 

484.6 

18 

2X 

19% 

142.52 

4.70 

2025.6 

2000.2 

1974.6 

1949.2 

1923.8 

189 8.2 


Columns composed of a 14'X 148# Special Column Section (H14b) reenforced with 
cover plates of width and thickness given in table. 



































STEEL CONSTRUCTION 


197 


TABLE VII (Continued) 

Formula P = 16,000—70 — 

r 

in which P = unit stress in pounds per square inch 
r = radius of gyration in inches 
1 = length in inches 

To the left of heavy line values of — do not exceed 120 



OF COLUMNS IN FEET 


16 

18 

20 

22 

24 

28 

32 

36 

40 

Section 

Lb . 

per Ft . 

1054.2 

1019.0 

983.8 

948.6 

913.2 

842.8 

772.2 

701.8 

631.2 

284.0 

1080.2 

1044.2 

1008.2 

972.2 

936.2 

864.2 

792.2 

720.2 

648.2 

290.8 

1107.0 

1070.4 

1033.6 

997.0 

960.4 

887.0 

813.6 

740.4 

667.0 

297.6 

1133.0 

1095.6 

1058.2 

1020.8 

983.4 

908,6 

833.8 

759.0 

684.0 

304.4 

1159.8 

1121.8 

1083.8 

1045.6 

1007.6 

931.6 

855.4 

779.2 

703.2 

311.2 

1186.0 

1147.2 

1108.4 

1069.6 

1030.8 

953.2 

875.6 

798.0 

720.4 

318.0 

1212.2 

1172.6 

1133.0 

1093.6 

1054.0 

975.0 

896.0 

816.8 

737.8 

324.8 

1239.0 

1199.0 

1158.8 

1118.6 

1078.4 

998.2 

917.8 

837.6 

757.2 

331.6 

1265.2 

1225.4 

1183.6 

1142.6 

1101.8 

1020.0 

938.2 

856.6 

774.8 

338.4 

1291.6 

1250.0 

1208.4 

1166.8 

1125.2 

1042.0 

958.8 

875.6 

792.4 

345.2 

1326.4 

1286.0 

1245.8 

1205.6 

1165.4 

1084.8 

1004.4 

923.8 

843.4 

350.3 

1354.6 

1313.6 

1272.6 

1231.6 

1190.6 

1108.6 

1026.6 

944.6 

862.6 

357.5 

1382.6 

1340.8 

1299.2 

1257.4 

1215.8 

1132.2 

1048.8 

965.4 

882.0 

364.7 

1410.8 

1368.4 

1326.0 

1283.4 

1241.0 

1156.2 

1071.2 

986.4 

901.4 

372.0 

1439.8 

1396.6 

1353.6 

1310.6 

1267.4 

1181.4 

1095.2 

1009.0 

923.0 

379.2 

1488.0 

1424.2 

1380.4 

1336.6 

1292.8 

1205.4 

1117.8 

1030.2 

942.6 

386.4 

1496.2 

1451.8 

1407.2 

1362.8 

1318.2 

1229.2 

1140.2 

1051.2 

962.2 

393.6 

1524.6 

1479.4 

1434.2 

1389.0 

1343.8 

1253.2 

1162.8 

1072.4 

982.0 

400.9 

1552.8 

1507.0 

1461.0 

1415.0 

1369.2 

1277.2 

1185.4 

1093.6 

1001.8 

408.1 

1581.2 

1534.6 

1488.0 

1441.4 

1394.8 

1301.4 

1208.2 

1115.0 

1021.6 

415.3 

1630.0 

1584.8 

1539.6 

1494.2 

1449.0 

1358.4 

1267.8 

1177.2 

1086.8 

423.4 

1660.4 

1614.4 

1568.4 

1522.4 

1476.4 

1384.4 

1292.4 

1200.4 

1108.4 

431.0 

1690.6 

1643.8 

1597.2 

1550.4 

1503.8 

1410.4 

1316.8 

1223.4 

1130.0 

438.7 

1721.0 

1673.4 

1626.0 

1578.6 

1531.2 

1436.4 

1341.4 

1246.6 

1151.8 

446.3 

1751.2 

1703.0 

1655.0 

1606.8 

1558.6 

1462.4 

1366.2 

1269.8 

1173.6 

454.0 

1781.6 

1732.8 

1683.8 

1635.0 

1586.2 

1488.6 

1390.8 

1293.2 

1195.4 

461.6 

1812.0 

1762.4 

1712.8 

1663.4 

1613.8 

1514.6 

1415.6 

1316.4 

1217.4 

469.3 

1842.4 

1792.2 

1741.8 

1691.6 

1641.4 

1540.8 

1440.4 

1339.8 

1239.4 

476.9 

1872.8 

1821.8 

1770.8 

1720.0 

1669.0 

1567.0 

1465.2 

1363.4 

1261.4 

484.6 


Weight 



























198 


STEEL CONSTRUCTION 









































STEEL CONSTRUCTION 


199 


TABLE VII (Continued) 

Formula P = 16,000 — 70 — 

r 

in which P = unit stress in pounds per square inch 
r = radius of gyration in inches 
I = length in inches 

To the left of heavy line values of ^ do not exceed 120 


OF COLUMNS IN 

FEET 








Weight 

15 

16 

18 

20 

22 

24 

28 

32 

36 

40 

Section 

Lb. 

per Ft. 

302.6 

296.6 

284.8 

273.0 

261.0 

249.2 

225.6 

201.8 

178.2 

154.6 

83.5 

331.6 

325.2 

312.2 

299.4 

286.4 

273.6 

247.8 

222.0 

196.2 

170.6 

91.0 

360.4 

i 

353.4 

339.4 

325.4 

311.6 

297.6 

269.6 

241.8 

213.8 

186.0 

99.0 

389.8 

382.2 

367.2 

352.4 

337.4 

322.4 

292.4 

262.4 

232.4 

202.6 

106.5 

419.0 

410.8 

394.8 

378.8 

362.8 

346.8 

314.6 

282.6 

250.4 

218.4 

114.5 

448.8 

440.2 

423.2 

406.0 

389.0 

372.0 

337.8 

303.8 

269.6 

235.6 

122.5 

478.2 

469.2 

451.0 

433.0 

414.8 

396.8 

360.6 

324.2 

288.0 

251.8 

130.5 

506.6 

497.0 

478.0 

459.0 

440.0 

420.8 

382.8 

344.6 

306.6 

268.4 

138.0 

536.4 

526.4 

506.2 

486.2 

466.2 

446.0 

405.8 

365.6 

325.4 

285.2 

146.0 

567.0 

556.6 

535.4 

514.4 

493.2 

472.2 

430.0 

387.8 

345.6 

303.4 

154.0 

597.2 

586.2 

564.0 

542.0 

519.8 

497.6 

453.4 

409.0 

364.8 

320.6 

162.0 

628.4 

616.8 

593.6 

570.4 

547.4 

524.2 

478.0 

431.8 

385.4 

339.2 

170.5 

658.8 

646.8 

622.6 

598.4 

574.4 

550.2 

501.8 

453.4 

405.2 

356.8 

178.5 

689.6 

677.0 

651.8 

626.6 

601.4 

576.2 

525.8 

475.4 

425.0 

374.6 

186.5 

721.2 

708.2 

682.0 

655.8 

629.6 

603.4 

551.0 

498.6 

446.4 

394.0 

195.0 

752.4 

738.8 

711.6 

684.4 

657.0 

629.8 

575.4 

521.0 

466.6 

412.2 

203.5 

781.8 

767.6 

739.4 

711.2 

683.2 

655.0 

598.6 

542.2 

485.8 

429.4 

211.0 

813.2 

798.6 

769.4 

740.2 

711.0 

681.8 

623.2 

564.8 

506.4 

448.0 

219.5 

844.8 

829.6 

799.4 

769.2 

739.0 

708.6 

648.2 

587.6 

527.2 

466.8 

227.5 

877.2 

861.6 

830.4 

799.2 

768.0 

736.8 

674.4 

612.0 

549.6 

487.2 

236.0 

909.4 

893.2 

861.0 

828.8 

796.6 

764.2 

699.8 

635.4 

570.8 

506.4 

244.5 

941.4 

924.8 

891.6 

858.4 

825.0 

791.8 

725.2 

658.8 

592.2 

525.8 

253.0 

C73.8 

956.6 

922.4 

888.0 

853.8 

819.4 

751.0 

682.4 

613.8 

545.2 

261.5 

1007.0 

989.4 

954.2 

919.0 

883.6 

848.4 

778.0 

707.6 

637.2 

566.8 

270.0 

1039.8 

1021.6 

985.4 

949.2 

912.8 

876.6 

804.2 

731.6 

659.2 

586.8 

278.5 

1 072.6 

1054.0 

1016.6 

979.4 

942.2 

904.8 

830.4 

755.8 

681.4 

606.8 

287.5 




3 































200 


STEEL CONSTRUCTION 






i 


TABLE VII (Continued) 

Safe Loads on Bethlehem Columns 

12' H-Section 

Safe loads are given in Thousands of Pounds 



-fH 

c 









Section 

Number 

Weight 

Section 

Lb. 

per Foot 

Dimension. Inches 

Area of 
Section 
Sq.In. 

Least 
Radius 
of Gyr. 
Inches 

UNSUPPORTED LENGTH 

D 

T 

B 

10 

11 

12 

13 

14 



64.5 

1154 

V 

11.92 

19.00 

2.98 

250.4 

245.0 

239.8 

234.4 

229.0 



71.5 

ny 8 

H 

11.96 

20.96 

3.00 

276.6 

270.8 

265.0 

259.0 

253.2 



78.0 

12 

3 A 

12.00 

22.94 

3.01 

303.0 

296.6 

290.2 

283.8 

277.4 



84.5 

12 'A 

H 

12.04 

24.92 

3.03 

329.6 

322.8 

315.8 

309.0 

302.0 



91.5 

12J4 

y 9 

12.08 

26.92 

3.04 

356.4 

348.8 

341.4 

334.0 

326.6 



98.5 

1254 

« 

12.12 

28.92 

3.06 

383.4 

375.4 

367.4 

359.6 

351.6 



105.0 

12 H 

i 

12.16 

30.94 

3.07 

410.4 

402.0 

393.4 

385.0 

376.6 

H12 

112.0 

12 H 

ia 

12.20 

32.96 

3.08 

437.4 

428.4 

419.4 

410.6 

401.6 



118.5 

\2% 

154 

12.23 

34.87 

3.10 

463.4 

454.0 

444.6 

435.0 

425.6 



125.5 

12 V* 

l A 

12.27 

36.91 

3.11 

490.8 

480.8 

471.0 

461.0 

451.0 



132.5 

13 

154 

r" 

12.31 

38.97 

3.13 

519.0 

508.4 

498.0 

487.6 

477.2 

- 


139.5 

1354 

1A 

12.35 

41.03 

3.14 

546.8 

535.8 

524.8 

513.8 

502.8 



146.5 

13M 

154 

12.39 

43.10 

3.15 

574.6 

563.2 

551.6 

540.2 

528.6 



153.5 

1354 

lA 

12.43 

45.19 

3.16 

603.0 

591.0 

578.8 

566.8 

554.8 



161.0 

1354 

154 

12.47 

47.28 

3.18 

631.6 

619.2 

606.6 

594.2 

581.6 
































STEEL CONSTRUCTION 


201 


TABLE VII (Continued) 

Formula P = 16,000—70— 

r 

in which P = unit stress in pounds per square inches 
r = radius of gyration in inches 
i = length in inches 

To the left of heavy line values of do not exceed 120 



OF COLUMNS IN FEET 

Weiaht 

15 

16 

18 

20 

22 

24 

28 

32 

36 

Section 

Lb. 

per Foot 

223.6 

218.4 

207.0 

196.8 

186.2 

165.4 

154.0 

132.6 

111.2 

64.5 

247.4 

241.4 

229.8 

21S.0 

206.2 

194.0 

171.0 

147.6 

124.0 

7*1.5 

271.0 

264.6 

251.8 

239.0 

226.2 

213.4 

187.8 

162.2 

136.6 

78.0 

295.0 

2S8.2 

274.4 

260.6 

246.8 

233 0 

205.2 

177.6 

150.0 

84.5 

319.2 

31 IS 

296.8 

282.0 

267.0 

252.2 

222.4 

192.6 

163.0 

91.5 

343.6 

335.6 

319.8 

304.0 

288.0 

272.2 

240.4 

208.6 

177.0 

98.5 

368.0 

359.6 

342.6 

325.8 

30S.S 

291.8 

258.0 

224.2 

190.2 

105.0 

392.6 

383.6 

365.6 

347.6 

329.6 

311.6 

375.6 

239.8 

203.8 

112.0 

416.2 

406.8 

3S7.S 

369.0 

350.0 

331.2 

293.4 

255.6 

217.8 

118.5 

441.0 

431.0 

411.2 

391.2 

371.2 

351.2 

311.4 

271.6 

231.6 

125.5 

466.0 

456.2 

435.2 

414,1 

393.4 

372.6 

330.6 

288.8 

247.0 

132.5 

491.8 

4S0.S 

459.0 

437.0 

415.0 

393.0 

349.2 

305.2 

261.4 

139.5 

517.2 

505.S 

4S2.8 

459.8 

436.8 

413.8 

367.8 

321.8 

275.8 

146.5 

542.8 

530.S 

506.8 

482.8 

458.8 

434.S 

386.6 

338.0 

290.6 

153.5 

569.2 

556.6 

531.6 

506.6 

4S1.8 

456.S 

400.8 

356.8 

306.8 

161.0 








































202 


STEEL CONSTRUCTION 





* 


TABLE VII (Continued) 

Safe Loads on Bethlehem Columns 

10' H-Section 

Safe loads are given in Thousands of Pounds 





3 




Section 

Number 

Weight 

Section 

Lb. 

per Ft. 

Dimensions. Inches 

Area of 
Section 
Square 
Inches 

Least 
Radius 
of Gyr. 
Inches 

UNSUPPORTED LENGTH 

D 

T 

B 

10 

11 

12 

13 

14 


49.0 

9% 

-fa 

9.97 

14.37 

2.49 

181.4 

176.6 

171.8 

167.0 

162.0 


,54.0 

10 

% 

10.00 

15.91 

2.51 

201.4 

196.0 

190.6 

185.4 

180.0 


59.5 

10 X 

H 

10.04 

17.57 

2.53 

222.8 

217.0 

211.2 

205.2 

199.4 


65.5 

10K 

X 

10.08 

19.23 

2.54 

244.0 

237.8 

231.4 

225.0 

218.6 


71.0 

10 H 

tt 

10.12 

20.91 

2.56 

266.0 

259.0 

252.2 

245.4 

238.6 


77.0 

io'A 

14 

10.16 

22.59 

2.57 

287.6 

280.2 

272.8 

265.4 

258.0 


82.5 

10 h 

H 

10.20 

24.29 

2.58 

309.6 

301.6 

293.8 

285.8 

278.0 


88.5 

10 X 

l 

10.24 

25.99 

2.60 

331.8 

323.4 

315.0 

306.6 

298.2 

H10 

94.0 

10 H 

liV 

• 

10.28 

27.71 

2.61 

354.2 

345.2 

336.4 

327.4 

318.6 


99.5 

li 

i X 

10.31 

29.32 

2.62 

375.2 

365.8 

356.4 

347.0 

337.6 


105.5 

ny 8 

1A 

10.35 

31.06 

2.64 

398.2 

388.2 

378.4 

368.4 

358.6 


111,5 

i m 

IX 

10.39 

32.80 

2.65 

420.8 

410.4 

400.0 

389.6 

379.2 


117.5 

11 H 

l A 

10.43 

34.55 

2.66 

443.6 

432.8 

421.8 

411.0 

400.0 


123.5 

liH 

l X 

10.47 

36.32 

2.67 

466.8 

455.4 

444.0 

432.6 

421.2 


l 













































STEEL CONSTRUCTION 


203 


TABLE Vll (Continued) 

Formula P = 16,000-70- 

r 

in which P=unit stress in pounds per square inch 
r = radius of gyration in inches 
l — length in inches 

To the left of heavy line values of — do not exceed 120 

r 










^ -l 





k 

4 

C) 





4 

- 8 - 4 

OF COLUMNS IN FEET 

Weight 












Section 

15 

16 

18 

20 

22 

24 

26 

28 

30 


Lb. 

per Ft. 

157.2 

152.4 

142.6 

133.0 

123.2 

113.6 

103.8 

94 J2 

84.4 

49.0 

174.6 

169.4 

158.8 

148.0 

137.4 

126.8 

116.2 

105.4 

94.8 

54.0 

193.6 

187.8 

176.2 

164.4 

152.8 

141.2 

129.4 

117.8 

106.2 

59.5 

212.2 

206.0 

193.2 

180.4 

167.8 

155.0 

142.4 

129.6 

116.8 

65.5 

231.6 

224.8 

211.0 

197.4 

183.6 

169.8 

156.2 

142.4 

128.8 

71.0 

250.6 

243.4 

228.6 

213.8 

199.0 

184.2 

169.4 

154.8 

140.0 

77.0 

270.0 

' 262.2 

246.2 

230.4 

214.6 

198.8 

183.0 

167.2 

151.4 

82.5 

289.8 

281.4 

264.6 

248.0 

231.2 

214.4 

197.6 

180.8 

164.0 

88.5 

309.6 

300.6 

282.8 

265.0 

247.2 

229.4 

211.4 

193.6 

175.8 

94.0 

328.2 

318.8 

300.0 

281.2 

262.4 

243.6 

224.8 

206.0 

187,2 

99.5 

348.8 

338.8 

319.0 

299.4 

279.6 

269.8 

240.0 

220.2 

200.4 

105.5 

368.8 

358.4 

337.6 

316.8 

296.0 

275.2 

254.4 

233.6 

212.8 

111.5 

389.2 

378.2 

356.4 

334.6 

312.8 

291.0 

269.2 

247.4 

225.4 

117.5 

409.8 

398.2 

375.4 

352.6 

329.8 

306.8 

284.0 

261.2 

238.4 

1 

123.5 
































204 


STEEL CONSTRUCTION 


Tfr* 





-- B -> 



TABLE VII (Continued) 

Safe Loads on Bethlehem Columns 

8" H=Section 

Safe loads are given in Thousands of Pounds 


Section 

N umber 

Weight 

Dimensions. Inches 

.irea of 
Section 
Sq. In. 

Least 

UNSUPPORTED LENGTH 

Section 

Lb. 

per Ft. 

D 

T 

B 

Radius 
of Gyr. 
Inches 

S 

9 

10 

11 

12 


31.5 

7H 

16 

8.00 

9.17 

1.98 

115.0 

111.8 

107.8 

104.0 

100.0 


34.5 

8 

H 

8.00 

10.17 

2.01 

128.8 

124.4 

120.2 

110.0 

111.8 


39.0 

8 Vs 

9 

16 

8.04 

11.50 

2.03 

146.0 

141.2 

136.4 

131.6 

126.8 


43.5 

sm 

H 

8.0S 

12.83 

2.04 

163.0 

157.8 

152.4 

147.2 

141.8 


48.0 

SH 

11 

16 

8.12 

14.18 

2.05 

180.4 

174.6 

16S.S 

163.0 

157.2 


53.0 

S'A 

Va 

8.16 

15.53 

2.07 

198.0 

191.8 

1S5.4 

179.2 

172.8 


57.5 

8 X 

13 

16 

8.20 

16.90 

2.08 

215.8 

209.0 

202.2 

195.4 

188.4 


62.0 

SK 

Vs 

S.24 

1S.27 

2.09 

233.6 

226.2 

218.8 

211.6 

204.2 

H8 

67.0 

8Vs 

15 

16 

8.28 

19.06 

2.11 

252.0 

244.2 

236.2 

228.4 

220.6 


71.5 

9 

1 

8.32 

21.05 

2.12 

270.0 

261.8 

253.4 

245.0 

236.8 


76.5 

9K 

Ws 

8.36 

22.46 

2.13 

2S8.4 

279.6 

270.8 

262.0 

253.0 


81.0 

9 H 

i K 

8.39 

23.78 

2.14 

305.8 

296.4 

287.2 

277.8 

268.4 


85.5 

9 n 

1i 3 6 

8.43 

25.20 

2.16 

324.8 

315.0 

305.2 

295.4 

285.6 


90.5 

9M 

IK 

8.47 

26.64 

2.17 

343.8 

333.4 

323.2 

312.8 

302.4 




















































STEEL CONSTRUCTION 


205 


TABLE VII (Continued) 

Formula P= 16,000 — 70- 

r 

in which P = unit stress in pounds per square inch 

r = radius of gyration in inches 
( = length in inches 

To the left of heavy line values of —do not exceed 120 

r 




OF COLUMNS IN FEET 







Weight 

13 

14 

15 

16 

17 

18 

20 

22 

24 

Section 

Lb. 

per Foot 

96.2 

92.2 

88.4 

84.4 

80.6 

76.6 

69.0 

61.0 

53.4 

31.5 

107.4 

103.2 

99.0 

94.8 

90.4 

86.2 

77.8 

69.2 

60.8 

34.5 

122.2 

117.4 

112.6 

107.8 

103.2 

98.4 

88.8 

79.4 

69.8 

39.0 

136.6 

131.4 

126.0 

120.8 

115.4 

110.2 

99.6 

89.0 

78.4 

43.5 

151.4 

145.6 

139.8 

134.0 

128.2 

122.2 

110 6 

99.0 

87.4 

48.0 

166.6 

160.2 

154.0 

147.6 

141.4 

135.0 

122.4 

109.8 

97.2 

53.0 

181.6 

174.8 

168.0 

161.2 

154.4 

147.6 

133.8 

120.2 

106.6 

575 

196.8 

189.6 

182.2 

174.8 

167.4 

160.2 

145.4 

130.8 

116.0 

62.0 

212.8 

205.0 

197.2 

189.4 

181.6 

173.6 

158.0 

142.4 

126.8 

67.0 

228.4 

220.0 

211.6 

203.4 

195.0 

186.6 

170.0 

153.4 

136.6 

71.5 

244.2 

235.4 

226.4 

217.6 

208.8 

200.0 

182.2 

164.4 

146.8 

76.5 

259.2 

249.8 

240.4 

231.2 

221.8 

212.4 

193.8 

175.2 

156.4 

81.0 

275.8 

266.0 

256.2 

246.4 

236.6 

226.8 

207.2 

187.6 

168.0 

85.5 

9QO 9 

281.8 

271.6 

261.2 

251 0 

240.6 

2200 

199.4 

178.8 

90.5 








































206 


STEEL CONSTRUCTION” 


TABLE VII (Continued) 

Safe Loads on Bethlehem Columns , 
Girder Beams Used as Columns 


Safe loads are given in Thousands of Pounds 


Section 

Number 

Depth 
of Beam 
Inobes 

Weight 
per Foot 
Pounds 

Area of 
Section 
Sq. In. 

Least 
Rad. of 
Gyr. In. 

UNSUPPORTED LENGTH 

8 

9 

10 

11 

12 

G30a 

30 

200 

58.71 

3.28 

819.0 

804.0 

789.0 

774.0 

759.0 

G30 

30 

180 

53.00 

2.86 

723.4 

708.0 

692.4 

676.8 . 

661.2 

G28a 

28 

180 

52.86 

3.18 

734.0 

720.G 

7C6.2 

692.2 

678.2 

G28 

28 

165 

48.47 

2.77 

658.0 

643.2 

628.6 

613.8 

599.2 

G26a 

26 

160 

46.91 

3.05 

647.2 

634.2 

621.4 

608.4 

595.6 

G26 

26 

150 

43.94 

2.68 

592.8 

579.0 

565.4 

551.6 

537.8 

G24a 

24 

140 

41.16 

2.90 

563.2 

551.2 

539.f 

527.4. 

515.4 

G24 

24 

120 

35.38 

2.66 

476.6 

465.6 

454.4 

443.2 

432.0 

G20a 

20 

140 

41.19 

2.91 

564.0 

552.0 

540.2 

528.2 

516.4 

G20 

20 

112 

32.81 

2.70 

443.2 

433.0 

422.8 

412.6 

402.4 

G18 

18 

92 

27.12 

2.59 

363.6 

354.8 

346.0 

337.2 

328.4 

G15b 

15 

140 

41.27 

2.83 

562.4 

550.0 

537.8 

525.6 

513.4 

G15a 

15 

104 

30.50 

2.64 

410.4 

400.6 

391.0 

381.2 

371.6 

G15 

15 

73 

21.49 

2.39 

283.4 

275.8 

268.4 

260.8 

253.2 

G12a 

12 

70 

20.58 

2.36 

270.6 

263.4 

256.0 

248.8 

241.4 

G12 

12 

55 

16.18 

2.24 

210.4 

204.2 

198.2 

192.2 

186.0 

G10 

10 

44 

12.95 

2.10 

165.8 

160.6 

155.4 

150.2 

145.0 

G9 

9 

38 

11.22 

1.98 

141.4 

136.6 

132.0 

127.2 

122.4 

G8 

8 

32.5 

9.54 

1.86 

118.2 

113.8 

109.6 

105.2 

101.0 


Beams not secured against yielding sideways and free to fail in direction of least radius 


of gyration. 
























STEEL CONSTRUCTION 


207 


TABLE VII (Continued) 

Formula P= 16,000 —70-^- 

r 

in which P = unit stress in pounds per square inch 
r = radius of gyration in inches 
( = length in inches. 

To the left of heavy line values of — do not exceed 120 

r 


OF COLUMNS IN FEET 


13 

14 

15 

16 

18 

743.8 

728.8 

713.8 

698.8 

668.8 

645.6 

630.0 

614.6 

599.0 

567.8 

664.2 

650.2 

636.4 

622.4 

594.4 

584.4 

569.8 

555.0 

540.4 

511.0 

582.6 

569.6 

556.8 

543.8 

518.0 

524.0 

610.2 

496.4 

482.6 

455.2 

503.6 

491.6 

479.8 

467.8 

444.0 

420.8 

409.6 

398.4 

387.4 

365.0 

504.4 

492.6 

480.6 

468.8 

445.0 

392.2 

382.0 

371.8 

361.6 

341.2 

319.6 

310.8 

302.0 

293.2 

275.6 

501.0 

488.8 

476.6 

464.4 

439.8 

•361.8 

352.2 

342.4 

332.8 

313.4 

245.6 

238.0 

230.6 

223.0 

207.8 

234.0 

226.8 

219.4 

212.0 

197.4 

180.0 

174.0 

167.8 

161.8 

149.6 

139.8 

134.6 

129.4 

124.4 

114.0 

117.6 

112.8 

108.2 

103.4 

93.8 

96.6 

92.4 

88.0 

83.8 

75.0 


20 


24 

28 

32 

1 per Ft. 

36 ! Pounds 

578.6 

518.4 

458.2 

398.0 i 

200 

474.4 

412.2 

349.8 

287.6 

180 

510.6 

454.8 

399.0 

343.0 

180 

422.8 

364.0 

305.2 


165 

440.4 

388.8 

337.2 


160 

372.6 

317.4 

262.4 


150 

372.4 

324.8 

277.0 


140 

298.0 

253.2 

208.6 


120 

373.6 

326.2 

278.6 


140 

2S0.0 

239.2 

198.4 


112 

222.8 

187.6 

152.4 


92 

366.4 

317.4 

268.4 


140 

255.0 

216.2 

177.4 


104 

162.6 

132.4 



73 

153.4 

124.2 



70 

113.2 

89.0 



55 

82.8 




44 




38 





32.5 


638.6 

536.6 

566.4 

481.6 

492.2 

427.6 

420.2 
3'42.6 

421.2 

320.8 

25S.0 

415.4 
294.0 

192.8 

182.8 

137.6 

103.6 


608.6 

505.6 

538.6 

452.2 

466.4 
400.0 

396.2 

320.2 

397.4 

300.4 

240.4 

390.8 

274.4 

177.6 

168.2 

125.4 


84.4 

66.4 


93.2 

74.8 

57.8 














































208 


STEEL CONSTRUCTION 


TABLE VII (Continued) 

Safe Loads on Bethlehem Columns 
I-Beams Used as Columns 
Safe Loads are given in Thousands of Pounds 


SeetioD 

Number 

Depth 
of Beam 
Inches 

Weight 
per Foot 
Pounds 

Area of 
Section 
Sq. In. 

Least 
Had. of 
Gyr. In. 

UNSUPPORTED LENGTH 

5 

6 

7 

8 

9 

10 

B30 

30 

120 

35.30 

2.16 

496.2 

482.4 

468 8 

455.0 

441.2 

427.6 

B28 

28 

105 

30.88 

2.06 

431.2 

418.6 

406.0 

393.4 

380.8 

368.2 

B26 

26 

90 

26.49 

1.95 

366.8 

355.4 

344.0 

332.6 

321.2 

309.8 

B24a 

24 

84 

24.80 

1.92 

342.6 

331.8 

320.8 

310.0 

299.2 

288.4 


24 

83 

24.59 

1.78 

335.4 

323.8 

312.2 

300.6 

289.0 

277.4 

B24 

24 

73 

21.47 

1.86 

295.0 

285.4 

275.6 

266.0 

256.2 

246.6 

B20a 

20 

82 

24.17 

1.82 

331.0 

319.8 

308.6 

297.4 

286.4 

275.2 


20 

72 

21.37 

1.88 

294.2 

284.6 

275.0 

265.6 

256.0 

246.4 


20 

69 

20.26 

1.59 

270.6 

260.0 

249.2 

238.6 

227.8 

217.2 

B20 

20 

64 

18.86 

1.62 

252.8 

243.0 

233.4 

223.6 

213.8 

204.0 


20 

59 

17.36 

1.66 

233.8 

225.0 

216.2 

207.4 

198.6 

190.0 


18 

59 

17.40 

1.50 

229.6 

220.0 

210.2 

200.4 

190.8 

181.0 

B18 

18 

54 

15.87 

1.54 

210.6 

202.0 

193.4 

184.6 

176.0 

167.4 


18 

52 

15.24 

1.56 

202.8 

194.6 

186.4 

178.2 

170.0 

161.8 


18 

48,5 

14.25 

1.59 

190.4 

182.8 

175.4 

167.8 

160.2 

152.8 

B15b 

15 

71 

20.95 

1.71 

283.8 

273.4 

263.2 

252.8 

242.6 

232.2 

B15a 

15 

64 

18.81 

1.49 

248.0 

237.4 

226.8 

216.2 

205.6 

195.0 


15 

54 

15.88 

1.55 

211.0 

202.4 

193.8 

185.2 

176.6 

168.0 


15 

46 

13.52 

1.36 

174.6 

166.2 

157.8 

149.6 

141.2 

132.8 

B15 

15 

41 

12.02 

1.41 

156.6 

149.4 

142.2 

135.0 

127.8 

120.8 


15 

38 

11.27 

1.44 

147.4 

140.8 

134.4 

127.8 

121.2 

114.6 

B12a 

12 

36 

10.61 

1.42 

138.4 

132.2 

125.8 

119.6 

113.2 

107.0 


12 

32 

9.44 

1.30 

120.6 

114.4 

108.4 

102.2 

96.2 

90.0 

B12 

12 

28.5 

8.42 

1.35 

108.6 

103.2 

98.0 

92.8 

87.6 

82.4 

BIO 

10 

28.5 

8.34 

1.21 

104.4 

98.8 

93.0 

87.2 

81.4 

75.6 


10 

23.5 

6.94 

1.27 

88.0 

83.4 

79.0 

74.4 

69.8 

65.2 


Beams not secured against yielding sideways and free to fail in direction of least radius 
of gyration. 


























STEEL CONSTRUCTION 


209 


TABLE VII (Continued) 

Formula P = 16,000-70- 

r 

in which P— unit stress in pounds per square inch 
r = radius of gyration in inches 

1 = length in inches 

To the left of heavy line values of — do not exceed 120 

OF COLUMNS IN FEET 

Weight 











per Foot 

11 

12 

13 

14 

15 

16 

18 

20 

22 

24 

Pounds 

I 413.8 

400.0 

386.4 

372.6 

358.8 

345.2 

317.6 

290.2 

262.8 

235.4 

120 

355.6 

343.0 

330.4 

317.8 

305.2 

292.6 

267.4 

242.2 

217.0 

191.8 

105 

298.4 

287.0 

275.4 

264.0 

252.6 . 

241.2 

218.4 

195.6 

172.8 


90 

277.4 

266.6 

255.8 

245.0 

234.0 

223.2 

201.6 

179.8 

158.2 


84 

265.8 

254.2 

242.6 

231.0 

219.4 

207.8 

184.6 

161.4 

138.2 


83 

236.8 

227.2 

217.4 

207.8 

198.0 

188.4 

169.0 

149.6 

130.2 


73 

2(54.0 

252.8 

241.6 

230.6 

219.4 

208.2 

186.0 

163.6 

141.4 


82 

236.8 

227.4 

217.8 

208.2 

198.6 

189.2 

170.0 

151.0 

131.8 


72 

206.4 

195.8 

185.0 

174.4 

163.6 

153.0 

131.4 

110.0 



69 

194.2 

184.4 

174.6 

164.8 

155.0 

145.2 

125.8 

106.2 



64 

181.2 

172.4 

163.6 

154.8 

146.0 

137.2 

119.6 

102.0 



59 

171.2 

161.4 

151.8 

142.0 

132.2 

122.4 

103.0 




59 

158.6 

150.0 

141.4 

132.8 

124.0 

115.4 

98.2 




54 

153.6 

145.4 

137.2 

129.0 

120.8 

112.6 

96.2 




52 

145.2 

137.6 

1302 

122.6 

115.0 

107.6 

92.4 




48.5 

222.0 

211.8 

201.4 

191.2 

180.8 

170.6 

150.0 




71 

184.4 

173.8 

163.2 

152.4 

141.8 

131.2 

110.0 




64 

159.4 

150.8 

142.2 

133.6 

125.0 

116.4 

99.2 




54 

124.4 

116.2 

107.8 

99.4 

91.0 

82.8 





46 

113.6 

106.4 

99.2 

92.0 

85.0 

77.8 





41 

108.0 

101.4 

94.8 

88.2 

81.8 

75.2 





3S 

100.8 

94.4 

£8.2 

81.8 

75.6 

69.4 





36 

84.0 

77.8 

71.8 

65.6 

59.6 






32 

77.0 

71.8 

66.6 

61.4 

56.2 






28.5 

69.8 

64.0 

58.2 

52.4 







28.5 

60.6 

56.0 

51.4 

46.8 







23.5 

1 . ' 




























210 


STEEL CONSTRUCTION 



TABLE VIII 

Safe Loads on Channel Columns 
6", 7", 8", 9", and 10" Channels 

Safe Loads are given in Thousands of Pounds 


2 Us 

2 Pis. 

r 

2 Pis 

Total 

8' 

9' 

10' 

11' 

12' 

13' 

6"-8# 

Latt. 

2 33 


4.76 

62 

61 

59 

57 

55 

54 

u 

3 

X 

CO 

2.32 

4.00 

8.76 

115 

112 

108 

105 

102 

99 

a 

A 

2.32 

5 00 

9.76 

128 

124 

121 

117 

114 

110 












7"-m 

Latt. 

2 72 


5 70 

77 

75 

74 

72 

70 

68 

u 

9Xi 

2.67 

4.50 

10.20 

tas 

134 

131 

128 

125 

122 

a 

A 

2.67 

5 63 

11.33 

153 

149 

145 

142 

138 

135 












8*-iu# 

Latt. 

3 11 


6.70 

93 

91 

89 

87 

85 

84 

a 

o 

X 

i»i>- 

3 03 

5.00 

11 70 

161 

158 

155 

152 

148 

145 

a 

A 

3.02 

6 25 

12.95 

178 

175 

171 

168 

164 

160 

a 

1 

3.01 

7 50 

14 20 

196 

192 

188 

184 

180 

176 












-8M3fF 

Latt. 

2 98 


8.08 

111 

109 

106 

104 

102 

100 

it 

10XA 

2 97 

6.25 

14 33 

197 

193 

189 

185 

181 

177 

it 

! 

2.96 

7.50 

15.58 

214 

210 

205 

201 

196 

192 













Latt. 

3.49 


7.78 

109 

107 

106 

104 

102 

100 

it 

nxl 

3 40 

5 50 

13 28 

186 

183 

180 

176 

173 

170 

it 

A 

3 as 

6.88 

14 66 

205 

202 

198 

195 

191 

187 

it 

1 

3.36 

8.25 

16 03 

224 

220 

216 

212 

208 

204 












9'-l 5# 

Latt. 

3 40 


8.82 

~TW~ 

121 

119 

117 

115 

113 

a 

11 xi 

3.36 

5 50 

14.32 

200 

197 

193 

190 

186 

183 

a 

A 

3.34 

6.88 

15.70 

220 

216 

212 

208 

204 

200 

a 

3 

H 

3.33 

8.25 

17 07 

239 

235 

230 

226 

221 

217 












10"-15# 

Latt. 

3 87 


8.92 

127 

125 

123 

121 

120 

118 

(4 

i^xA 

3 74 

7 50 

16.42 

233 

230 

226 

222 

218 

215 

it 

3 

8 

3 72 

9 00 

17.92 

254 

250 

246 

242 

238 

234 

it 

A 

3 70 

10 50 

19 42 

275 

271 

267 

262 

258 

253 

it 


3.68 

12 00 

20.92 

296 

292 

287 

282 

277 

272 












10’-20# 

Latt. 

3 66 


11.76 

167 

164 

161 

159 

156 

153 

44 

12X A 

3 64 

10 50 

22.26 

315 

310 

305 

300 

295 

289 

44 

h 

3 63 

12 00 

23 76 

336 

331 

325 

320 

314 

309 

it 

A 

3.62 

13.50 

25.26 

357 

351 

346 

340 

334 

328 

it 

A 

k 

3.61 

15 00 

26.76 

378 

372 

366 

360 

354 

348 






8' 

9' 

10' 

IV 

12' 

13' 


UNSUPPORTED LENGTH 




















































































































STEEL CONSTRUCTION 


211 


TABLE VIII (Continued) 


Formula 


P = 16,000 -70 - 
r 


in which P = unit stress in pounds per square inch 
r=radius of gyration in inches 
l = length in inches 

To left of heavy line values of-do not exceed 125 

r 

To right of heavy line values of — do not exceed 150 
r 



OF COLUMN IN FEET 


14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' | 26' 

28' 

30' 

52 

50 

49 

47 

45 

43 

41 

40 

38 

36 

35 

32 

28 


96 

93 

89 

86 

83 

80 

77 

74 

70 

67 

64 

58 

51 


107 

103 

100 

96 

93 

89 

86 

82 

78 

75 

71 

64 

57 
















67 

65 

63 

61 

601 58 

56 

54 

53 

51 

49 

45 

42 

1 38 

118 

115 

112 

109 

106 

102 

99 

96 

93 

90 

86 

80 

73 

67 

131 

128 

124 

121 

117 

113 

110 

106 

103 

99 

96 

89 

81 

74 















82 

80 

78 

76 

75 

73 

71 

69 

67 

66 

64 

60 

57 

53 

142 

139 

136 

132 

129 

126 

122 

119 

116 

113 

109 

103 

96 

90 

157 

153 

150 

146 

142 

139 

136 

132 

128 

124 

121 

113 

106 

99 

172 

168 

164 

160 

156 

152 

148 

144 

140 

136 

132 

124 

116 

108 















97 

95 

93 

91 

88 

86 

84 

81 

79 

77 

75 

70 

66 

61 

173 

169 

164 

160 

156 

152 

148 

144 

140 

136 

132 

124 

116 

108 

187 

183 

179 

174 

170 

165 

161 

156 

152 

148 

143 

134 

125 

117 















98 

96 

95 

93 

91 

89 

87 

85 

83 

81 

80 

76 

72 

68 

166 

163 

160 

157 

153 

150 

147 

144 

140 

137 

134 

127 

121 

114 

184 

180 

176 

173 

169 

165 

162 

158 

154 

151 

147 

140 

133 

125 

200 

196 

192 

188 

184 

180 

176 

172 

168 

164 

160 

152 

144 

136 















111 

108 

106 

104 

102 

100 

98 

95 

93 

91 

89 

85 

80 

76 

179 

175 

172 

168 

165 

161 

158 

154 

150 

147 

143 

136 

129 

122 

196 

192 

188 

184 

180 

176 

172 

168 

164 

160 

156 

149 

141 

133 

213 

209 

204 

200 

196 

192 

187 

183 

178 

174 

170 

161 

153 

144 















116 

114 

112 

110 

108 

106 

104 

102 

100 

98 

96 

92 

88 

85 

211 

207 

204 

200 

196 

193 

189 

185 

182 

178 

174 

167 

159 

152 

230 

226 

222 

218 

214 

210 

206 

202 

198 

194 

190 

182 

173 

165 

249 

244 

240 

236 

231 

227 

223 

218 

214 

209 

205 

196 

187 

178 

268 

263 

258 

254 

249 

244 

239 

235 

230 

225 

220 

211 

201 

191 















150 

148 

145 

142 

140 

"T37| 

134 

132 

129 

126 

123 

118 

113 

107 

284 

279 

274 

269 

264 

259 

253 

248 

243 

238 

233 

223 

212 

202 

303 

298 

292 

287 

281 

276 

270 

265 

259 

254 

248 

237 

226 

215 

322 

316 

310 

305 

299 

293 

287 

281 

275 

269 

263 

252 

240 

228 

341 

335 

329 

322 

316 

310 

304 

•297 

291 

•285 

279 

267 

254 

241 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 

















































































212 


STEEL CONSTRUCTION 



TABLE VIII (Continued) 

Safe Loads on Channel Columns 
12" Channels 

Safe Loads are given in Thousands of Pounds 


2 Cs 

2 Pis. 

T 

Area 

2 Pis. 

Area 

Total 

UNSUPPORTED LENGTH 

8' 

9' 

10' 

IV 

12' 

13' 

12"-20±# 

Latt. 

4.61 


12.06 

175 

173 

171 

169 

167 

164 

ii 

14XA 

4.40 

8.75 

20.81 

301 

297 

293 

289 

285 

281 

a 

3 

8 

4 38 

10 50 

22 56 

326 

322 

317 

313 

309 

304 

it 

7 

16 

4.35 

12 25 

24.31 

352 

346 

342 

337 

333 

328 

it 

1 

2 

4 33 

14 00 

26 06 

377 

371 

366 

361 

356 

351 












12"-25# 

Latt. 

4.43 


14.70 

213 

210 

207 

204 

202 

199 

it 

14XA 

4.30 

12.25 

26.95 

389 

384 

378 

373 

368 

363 

it 

1 

2 

4 29 

14.00 

28.70 

414 

409 

403 

397 

392 

386 

it 

9 

16 

4.27 

15.75 

30.45 

439 

433 

427 

421 

415 

409 

it 

5 

8 

4.26 

17.50 

32.20 

464 

458 

452 

445 

439 

433 

a 

11 

16 

4 25 

19.25 

33.95 

489 

483 

476 

469 

463 

456 

u 

3 

4 

4.24 

21.00 

35.70 

514 

507 

500 

493 

486 

479 












I2"-30# 

Latt. 

4.28 


17 64 

255 

251 

247 

244 

241 

237 

ti 

14X& 

4.23 

15.75 

33.39 

481 

474 

468 

461 

455 

448 

it 

5 

8 

4.22 

17.50 

35.14 

506 

499 

492 

485 

478 

471 

it 

11 

16 

4.21 

19.25 

36.89 

531 

524 

517 

509 

502 

494 

it 

3 

4 

4.20 

21.00 

38 64 

556 

549 

541 

533 

525 

518 

a 

H 

4.20 

22.75 

40 39 

582 

574 

566 

557 

549 

541 

a 

5 

4 19 

24.50 

42.14 

607 

598 

590 

581 

573 

564 

a 

15 

16 

4.18 

26.25 

43.89 

632 

623 

614 

605 

597 

588 

a 

1 

4 18 

28.00 

45.64 

657 

648 

639 

630 

620 

611 












12"-35# 

Latt. 

4 17 


20.58 

296 

292 

288 

284 

280 

276 

if 

14XH 

4 17 

19 25 

39.83 

573 

565 

557 

549 

541 

533 

it 

3 

4 

4 16 

21.00 

41.58 

598 

590 

581 

573 

565 

556 

it 

13 

16 

4 16 

22.75 

43 33 

623 

614 

606 

597 

588 

579 

ii 

7 

8 

4 15 

24.50 

45.08 

648 

639 

630 

621 

612 

603 

a 

1A 

16 

4.15 

26.25 

46.83 

674 

664 

655 

645 

635 

626 

a 

1 

4 14 

28 00 

48.58 

699 

689 

679 

669 

659 

649. 

a 

H 

4.14 

31 50 

52 08 

749 

738 

727 

717 

706 

696 

a 

H 

4.13 

35.00 

55 58 

799 

787 

776 

765 

753 

742 




























8' 

9' 

10' 

IV 

12' 

13' 

























































































STEEL CONSTRUCTION 


213 


TABLE VIII (Continued) 

Formula P= 16,000 -70- 

r ^ 

in which P=unit stress in pounds per square inch 

T = radius of gyration in inches 

1 = length in inches 

To left of heavy line values of — do not exceed 125 _ 

r 

To right of heavy line values of — do not exceed 150 

r 


p 

OF COLUMN IN FEET 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 

162 

160 

158 

156 

153 

151 

149 

147 

145 

142 

140 

136 

131 

127 

277 

273 

269 

265 

261 

257 

253 

250 

246 

242 

238 

230 

222 

214 

300 

296 

291 

287 

283 

279 

274 

270 

266 

261 

257 

248 

240 

231 

323 

318 

314 

309 

304 

300 

295 

290 

286 

281 

276 

267 

257 

248 

346 

341 

336 

331 

326 

321 

316 

311 

306 

301 

295 

285 

275 

265 















196 

193 

191 

188 

185 

182 

179 

177 

174 

171 

168 

163 

157 

152 

357 

352 

347 

342 

336 

331 

326 

321 

315 

310 

305 

294 

284 

273 

381 

375 

369 

364 

358 

352 

347 

341 

335 

330 

324 

313 

302 

291 

403 

397 

391 

385 

379 

373 

367 

361 

355 

349 

343 

331 

319 

308 

426 

420 

413 

407 

401 

394 

388 

382 

375 

369 

363 

350 

337 

325 

449 

442 

436 

429 

422 

416 

409 

402 

395 

389 

382 

369 

355 

342 

472 

465 

458 

451 

444 

437 

430 

423 

415 

408 

401 

387 

373 

359 















234 

230 

227 

223 

220 

216 

213 

210 

206 

203 

199 

192 

185 

178 

441 

435 

428 

421 

415 

408 

402 

395 

388 

382 

375 

362 

349 

335 

464 

457 

450 

443 

436 

429 

422 

415 

408 

401 

394 

380 

366 

352 

487 

480 

472 

465 

458 

450 

443 

436 

428 

421 

414 

399 

384 

370 

510 

502 

495 

487 

479 

471 

464 

456 

448 

440 

433 

417 

402 

386 

533 

525 

517 

509 

501 

493 

485 

477 

469 

460 

452 

436 

420 

404 

556 

548 

539 

531 

522 

514 

505 

497 

488 

480 

472 

455 

438 

421 

579 

570 

561 

552 

543 

535 

526 

517 

508 

499 

491 

473 

455 

438 

602 

593 

583 

574 

565 

556 

547 

538 

529 

519 

510 

492 

473 

455 















271 

267 

263 

259 

255 

250 

246 

242 

238 

234 

230 

221 

213 

205 

525 

517 

509 

501 

493 

485 

477 

469 

461 

453 

445 

429 

413 

397 

548 

539 

531 

523 

514 

506 

497 

489 

480 

472 

464 

447 

430 

413 

571 

562 

553 

545 

536 

527 

518 

510 

501 

492 

483 

466 

448 

431 

594 

584 

575 

566 

557 

548 

539 

530 

520 

511 

502 

484 

466 

448 

617 

607 

597 

588 

579 

569 

559 

550 

541 

531 

522 

503 

484 

465 

639 

629 

619 

610 

600 

590 

580 

570 

560 

550 

541 

521 

501 

481 

685 

675 

664 

653 

643 

632 

622 

611 

601 

590 

580 

558 

537 

516 

731 

720 

708 

697 

686 

674 

663 

652 

640 

629 

618 

595 

572 

550 





























14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 
















































































214 


STEEL CONSTRUCTION 



TABLE VIII (Continued) 

Safe Loads on Channel Columns 
12" and 15" Channels 

Safe Loads are given in Thousands of Pounds 


QQ 

U 

<N 

2 Pis. 

r 

Area 

2 Pis. 

Area 

Total 

UNSUPPORTED JLENGTH 

8' 

9' 

io' | ir 

12' 

13' 












l2"-40# 

Latt. 

4.09 


23.52 

338 

333 

328 

323 

318 

314 

ii 

14 XH 

4 12 

22.75 

46.27 

665 

655 

646 

636 

627 

618 

ii 

i 

4. 11 

24.50 

48.02 

690 

680 

670 

660 

651 

641 

ii 

n 

4. 11 

26.25 

49.77 

715 

705 

695 

684 

674 

664 

a 

i 

4.11 

28.00 

51.52 

740 

730 

719 

708 

698 

687 

a 

ii 

4.10 

31.50 

55.02 

790 

779 

768 

757 

745 

734 

ii 

H 

4.10 

35.00 

58.52 

840 

828 

816 

804 

792 

780 

a 

i! 

4.10 

,38.50 

62.02 

891 

878 

865 

853 

840 

827 

a 

n 

4.09 

42.00 

65.52 

941 

927 

914 

900 

887 

873 












15"-33# 

Latt. 

4.98 


19.80 

290 

287 

283 

280 

277 

273 

ii 

16X | 

4.84 

12.00 

31.80 

465 

459 

453 

448 

443 

437 

a 

tV 

4.83 

14.00 

33.80 

494 

488 

482 

476 

470 

464 

a 

h 

4.82 

16.00 

35.80 

523 

517 

510 

504 

498 

492 

a 

§ 

4.80 

20.00 

39.80 

581 

574 

567 

560 

553 

546 

a 

1 

4 

4.79 

24.00 

43.80 

639 

632 

624 

616 

609 

601 

a 

1 

4.76 

32.00 

51.80 

756 

747 

738 

728 

719 

710 

15"-35# 

Latt. 

4.94 


20.58 

301 

298 

294 

291 

"W 

284 

ii 

lttX I 

4.81 

16.00 

36.58 

534 

528 

521 

515 

508 

502 

a 

1 

4.79 

20 00 

40.58 

592 

585 

578 

571 

564 

557 

a 

i 

4.77 

24.00 

44.58 

650 

642 

635 

627 

619 

611 

a 

i 

4.75 

32 00 

52 58 

767 

758 

748 

739 

730 

720 

ii 

H 

4.72 

48.00 

68.58 

1000 

988 

975 

963 

950 

938 

15"-40#* 

Latt. 

4.84 


23.52 

344 

340 

335 

331 

327 

323 

a 

16 X h 

4.75 

16 00 

39 52 

576 

569 

562 

555 

548 

541 

a 

i 

4 74 

20.00 

43.52 

635 

627 

619 

611 

604 

596 

44 

1 

4 

4.73 

24.00 

47 52 

693 

684 

676 

668 

659 

651 

ii 

1 

4 71 

32 00 

55.52 

809 . 

799 

789 

780 

770 

760 

ii 

H 

4.69 

48 00 

71.52 

1042 

1029 

1016 

1003 

991 

978 

ii 

2 

4.68 

64.00 

87 52 

1274 

1259 

1243 

1227 

1211 

1196 

l5"-45# 

16 X 1 

4.69 

20 00 

46.48 

677 

669 

660 

652 

644 

635 

ii 

i 

4 68 

24.00 

50.48 

735 

726 

717 

708 

699 

690 

ii 

1 

4 68 

32.00 

58.48 

851 

841 

830 

820 

809 

799 

ii 

n 

4.66 

48.00 

74 48 

1084 

1071 

1058 

1044 

1031 

1017 

ii 

2 

4 66 

64 00 

90.48 

1317 

1301 

1285 

1268 

1252 

1235 

15"-50# 

16X1 

4 64 

32 00 

61.42 

894 

883 

872 

861 

849 

838 

a 

H 

4 64 

48.00 

77.42 

1126 

1112 

1098 

1084 

1070 

1056 

u 

2 

4.63 

64.00 

93 42 

1359 

1342 

1325 

1308 

1291 

1274 

a 

2? 

4 63 

80.00 

109 42 

1592 

1572 

1552 

1532 

1312 

1492 






8' 

9' 

10' 

11' 

12' 

13' 

















































































































































STEEL CONSTRUCTION 


215 


TABLE VIII (Continued) 

Formula P = 16,000 - 70 - 

T — 

in which P = unit stress in pounds per square inch 
r = radius of gyration in inches 
l = length in inches 

To left of heavy line values of - do not exceed 125 

To right of heavy line values of — do not exceed 150 

r 



OF COLUMNS IN FEET 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23' 

24' 

26' 

28' 

30' 















309 

304 

299 

294 

289 

285 

280 

275 

270 

265 

260 

251 

241 

231 

608 

599 

589 

580 

570 

561 

552 

542 

533 

523 

514 

495 

476 

457 

631 

621 

611 

602 

592 

582 

572 

562 

552 

543 

533 

513 

494 

474 

654 

644 

634 

624 

613 

603 

593 

583 

572 

562 

552 

532 

512 

491 

677 

666 

656 

646 

635 

624 

614 

603 

592 

582 

571 

551 

530 

509 

722 

711 

700 

689 

677 

666 

655 

644 

632 

621 

610 

587 

565 

542 

768 

756 

744 

732 

720 

708 

696 

684 

672 

660 

648 

624 

600 

576 

814 

802 

789 

776 

763 

751 

738 

726 

713 

700 

687 

662 

636 

611 

860 

846 

833 

820 

806 

793 

779 

766 

752 

739 

725 

698 

672 

645 















270 

267 

263 

260 

257 

253 

250 

247 

243 

240 

237 

230 

223 

217 

432 

426 

420 

415 

409 

404 

398 

393 

387 

382 

376 

365 

354 

343 

458 

453 

447 

441 

435 

429 

423 

417 

411 

406 

400 

388 

376 

364 

485 

479 

473 

467 

460 

454 

448 

442| 435 

429| 423 

411 

398 

386 

539 

532 

525 

518 

511 

504 

497 

490| 483 

476 

470 

456 

442 

428 

593 

586 

578 

570 

562 

555 

547 

540 

532 

524 

516 

501 

486 

470 

701 

692 

683 

673 

664 

655 

646 

637 

628 

619 

609 

591 

573 

554 

280 

277 

273 

270 

266 

263 

259 

256 

252 

249 

245 

238 

231 

224 

• 496 

489 

483 

477 

470 

464 

458 

451 

445 

438 

432 

419 

406 

394 

549 

542 

535 

528 

521 

514 

‘ 507 

500 

493 

486 

478 

464 

450 

436 

603 

596 

588 

580 

572 

564 

556 

548 

541 

533 

525 

509 

494 

478 

711 

702 

693 

683 

674 

665 

655 

646 

637 

627 

618 

599 

581 

562 

926 

914 

902 

890 

878 

866 

853 

841 

828 

816 

804 

780 

756 

731 

319 

315 

311 

307 

303 

299 

295 

290 

286 

282 

278 

270 

262 

254 

534 

527 

520 

513 

506 

499 

492 

485 

478 

471 

464 

450 

436 

422 

588 

581 

573 

565 

557 

550 

542 

534 

527 

519 

511 

496 

480 

465 

642 

634 

625 

617 

608 

600 

592 

583 

575 

566 

558 

541 

524 

507 

750 

740 

730 

720 

710 

700 

690 

680 

671 

661 

651 

631 

611 

591 

965 

952 

939 

926 

914 

901 

888 

875 

863 

850 

837 

811 

785 

760 

1181 

1165 

1149 

1133 

1118 

1102 

1086 

1070 

1055 

1039 

1023 

992 

960 

929 

627 

619 

610 

602 

594 

586 

577 

569 

561 

552 

544 

527 

510 

494 

681 

672 

663 

654 

645 

636 

626 

617 

608 

599 

590 

572 

554 

536 

789 

778 

768 

757 

747 

736 

726 

715 

705 

694 

684 

663 

642 

620 

1003 

990 

976 

963 

950 

936 

923 

909 

896 

883 

869 

842 

816 

789 

1219 

1202 

1186 

1170 

1154 

1137 

1121 

1105 

1088 

1072 

1056 

1023 

991 

958 

827 

816 

805 

794 

783 

771 

760 

749 

738 

727 

716 

693 

671 

649 

1042 

1028 

1014 

1000 

986 

972 

958 

944 

930 

916 

902 

874 

846 

818 

1257 

1241 

1224 

1206 

1189 

1172 

1156 

1139 

1122 

1105 

1087|1054 

1020 

987 

1473 

1453 

1433 

1413 

1393 

1373 

1354 

1334 

1314 

1294 

127411234 

1195 

1156 

14' 

15' 16' 

17' 18' 19' 20' 21' 

22' | 23' 

24' | 26' 

28' 

30' 









































































































216 


STEEL CONSTRUCTION 


Details of Construction. 

stack may be made 


in one- 




r 



[>—<!► 


c 


jnPL taxi' 


rn l4 x y 


PL >4Ag 



Fig. 145. Splice in a Channel Column 


Splices. The several columns in a 
two-, or three-story lengths. Two- 
story lengths are most commonly 
used. The one-story length per¬ 
mits each story of the column to 
be designed for the load in that 
story, whereas a two-story col¬ 
umn is designed for the load in 
the lower of the two stories, the 
same section being used through¬ 
out the two-story length; this 
gives a greater area in the upper 
story than is required for the 
stress in that story. Similarly, 
for the three-story column the 
middle and upper stories are ex¬ 
cessive; also the three-story col¬ 
umn is more difficult to erect. 
The saving in favor of the one-story column is offset by the expense 
of the splices for material, shop' labor, and erection; hence the 
common use of the two-story lengths. 

The splice is placed above the floor line a sufficient distance so 

that the splice plates will not in¬ 
terfere with the beam connec¬ 
tions; usually 18 inches is enough 
space. The strength of the splice 
plates may vary from a nominal 
amount to the full strength of the 
column, generally the former, it 
being considered that the splice 
plates serve only to hold the col¬ 
umns rigidly in line. Even when 
there is bending stress due to 
eccentric loads, it seldom hap¬ 
pens that there is actual tension 
on one side of the column, hence 
the splice plates do not transmit 
any stress. 


Zi 


<t> 


'PL 'OX# 

4 L s SXJ/Sg - 

/Of ^ £ 

frn LtfX g 


4> 




P4 


4 'll" 


-"I, 

; in 


bvt-.lliliV.t-. 

n 




Si 


Q I 

. I i| 
<t> Ijl 

—-H- 


Fig. 14G. 


I PL IP"*B 
4 L 5 6 X4 X,i 

Splice in a Plate and Angle Column 



























































































STEEL CONSTRUCTION 


217 


As the splice plates are not designed to carry stress, the load 
must be transmitted by direct bearing of the upper column on the 
lower. This requires that the ends be milled exactly at right angles 
to the axis of the columns and that the end of the upper column 
have full bearing on the top of the lower column, or, if this cannot 
be had on account of change in size or shape of columns, then that 
a bearing plate be used between the column sections. 

Fig. 145 shows a column splice in which the upper section of 
column rests directly on the lower section. The splice is made by 
means of the plates m and the angles o. The plates n are fillers 
which make up the difference in width of the two sections of column. 
The angles o are used on the web of the channels because plates 
could not be riveted on after the columns are in place. 

Fig. 146 shows a column splice in which the upper section of 
column does not rest directly, on the lower section. In addition to 



Fig. 147. Types of Lacing for Columns 


the splice plates m, there are required the filler plates n, the bearing 
plate p, and the connection angles o. 

No rules can be given for the thickness of splice plates, but they 
should be made consistent with the column section. 

Riveting. The specifications for riveting, p. 365, govern the 
rivet spacing in columns. Refer to these specifications and note 
the spacing at the ends and the maximum spacing. It is interesting, 
as an indication of relative cost, to note the number of lines of rivets 
required for various styles of columns as follows: 

Plate and angle columns without cover plates... .2 rows 
Plate and angle columns with cover plates. . 4 or 6 rows 


Channel columns.4 rows 

Bethlehem columns with cover plates.4 rows 

Zee-bar columns without cover plates.2 rows 

Zee^bar columns with cover plates... \.6 rows 


Lacing . Schneider’s Specifications* contain provisions regard-' 

•“Specifications for Structural Steel for Buildings’*, by C. C. Schneider, M. Am. Soc. C. E., 
Transactions American Society of Civit Engineers % Vol. LIV, p. 449. 
































218 


STEEL CONSTRUCTION 


ing lattice bars, p. 365. Fig. 147 shows the style of lacing referred' 
to. At the ends of laced columns tie plates are required. These, 
plates should have a length not less than the width of the member. 
Tie plates must also be used where beams connect to the column 
and when the lacing must be omitted for any cause. 

Connections. Connections for beams and girders are described 
and illustrated under the discussion of beams and girders. The 
methods there given will enable the designer to work out any special 
connections required. 

Brackets. Brackets projecting to a considerable distance from 
the face of columns are used for supporting cornices, balconies, etc. 

v. 

If the bracket is constructed with a solid web plate and with parallel 
flanges, it may be designed as a cantilever girder. The bracket may 



4 '- 0 " 


wooo. 



Fig. 148. Bracket on Column 



be made up of a tie and a strut, Fig. 148, with no web plate. In 
this case the stresses are determined by the methods given in “Stat¬ 
ics”. To illustrate, use the data given in Fig. 148-a and the stress 
diagram, Fig. 148-b. For a load of 18,000 pounds on the end of the 
bracket, the stress in the tie is 18,000 pounds and the stress in the 
strut is 25,200 pounds. The tie and strut can now be designed by 
the methods given for tension and compression members. It is very 
important to keep in mind that loads on all projecting brackets are 
eccentric loads on the columns and the columns must be designed 
accordingly 

Bases. As the allowable pressure on the masonry foundation 
of the column is very much less than the stress in the column, it is 














STEEL CONSTRUCTION 


219 


necessary to provide a base plate to spread the load over the required 
area of the masonry. Whatever the form of base used, the bottom 
of the column section must be milled and the top of the base must 
be also a flat surface. If a steel plate is used, it will be true enough 
without milling, but all other forms require milling to give a true 
top surface. Two or more angles are riveted to the bottom of the 
column to provide a means of bolting the column to the base, Fig. 
149. This bolting is done chiefly for assistance in erection. 



Fig. 149. Details of Bottom of Column 


The bases are usually set exactly to elevation and alignment 
before the columns are set. This makes it easy to get the columns 
in their correct position. The bases are first supported on wedges 
and then the space under them grouted. 

Flat Plates . The simplest form of column base is a flat plate, 
which may be either steel or cast iron. Having the load on the 
column and the allowable unit pressure on the masonry, the area 













































































































220 


STEEL CONSTRUCTION 


of the plate is computed therefrom. The thickness of the plate is 
computed in the same manner as bearing plates for beams, p. 130. 

The thickest steel plate ordinarily available is 1 inch and this 
limits the size of steel plate that can be used. However, steel slabs 
up to 12 inches thick can be had from the rolling mills if the quan¬ 
tity is large and considerable time can be allowed for delivery. They 
are designed in the same manner as plates of ordinary thickness 
except that the unit stress from bending should be 14,000 pounds 
per square inch. There is not likely to be any economy in using 
steel slabs when there is room for using cast-iron pedestals. 

Cast-iron plates can be made of any thickness, but when the 
thickness would be greater than 4 inches, it becomes economical to 
use cast-iron pedestals. Fig. 150 is a cast-iron plate. The hole in 
the center is for grouting. In this form of plate the bolts must be 

in place before the plate is set; 
the bottom of the plate is 
recessed for the bolt heads. 

Cast-Iron Pedestals. When 
the size of the required base 
is so great that a flat plate is 
not practicable, the cast-iron 
pedestal is used, Fig. 151. It 
is impossible to compute the 
stresses in a cast-iron pedestal 
with any certainty. However, 
it is customary to design them 
by the flexure formula, which 
seems to give results that are satisfactory. This cannot be done 
directly, hence the dimensions must be assumed or determined from 
other considerations, and the resulting section checked by computing 
its resisting moment. 

Illustrative Example. Assume that the load on a column is 
600,000 pounds and the unit bearing on masonry is 500 pounds per 
square inch. Then the area required is 



BOLT HEAD 

Fig. 150. Cast-Iron Base Plate 


600,000 

500 


= 1200 sq. in. 


Use a plate 3'-0"X3'-0'', which gives an area slightly in excess 
pf the amount required. 








































































































































222 


STEEL CONSTRUCTION 


The size of the top plate is determined by the size of the column 
and its connection angles. In this case assume 20 inches. 

The height must be assumed. It may vary between one-third and 

one-half the base. Use 16 inches. 

The diameter of the hub is 
assumed. Use 8 inches inside. 

The thickness of metal must 
be assumed for trial. Use lf-inch 
for hub; If inches for top plate; 
and If inches for base plate. 

The shaded area in Fig. 152 
shows the section available for 
resisting bending. To determine 
its resisting moment R M it is first necessary to locate its neutral 
axis and then compute its moment of inertia. 

The center of gravity is found by the method given on p. 36. 
The area of the cross section is 



Fig. 152. 


Section for Computing Strength of 
Cast-Iron Pedestals 


for a 

area=33"X If" 

= 57.75 

for b 

area= 2"Xl3"Xlf" 

= 32.50 

for d 

area= 2"X6"Xlf" 

= 15.00 


105.25 sq. in. 


Taking moments about the bottom line 

fora moment = 57.75 X .875= 50.53 
for b moment = 32.50X 8.25 =268.12 
for d moment = 15.00X15.375 = 230.62 

549.27 

The distance from the bottom of the plate to the neutral axis 0-0 is 

549.27 


C r 


5.21" 


105.25 

The moment of inertia about the axis 0-0 is 

/from tables 


for a 


for b 


for d 


/ = 


\57.75X(4.33) 5 

/from tables 
\32.50 X (3.04) 5 

x /from tables 
i_ \l5X(10.16) a 


15 

1083 

458 

301 

2 

1548 

3407 













































STEEL CONSTRUCTION 


223 


The allowable stress on east iron in tension is 3000 pounds per 
square inch. Then the resisting moment of the section is 


R M = S- = 30n ?*f 4 07 .1,940,000 in.-lb. 
c 5.21 


The bending moment M, resulting from the pressure on the 
bottom of the plate, is determined by treating the plate as an 
inverted cantilever, Fig. 152. 

Then M = 300,000X9 = 2,700,000 in.-lb. 

• This amount is excessive because it assumes the column load applied 
at a point at the center of the top of the plate, whereas it occupies 
considerable area. 

As the bending moment computed for the load is 2,700,000 
inch-pounds and the resisting moment is 1,940,000 inch-pounds, the 
trial section is not sufficient. The section can be increased in 
strength by increasing the height or by increasing the thickness of 
metal. The most effective places for additional metal are in the 
top and bottom plates. 

Problem 

Increase the height of the cast-iron pedestal to l'-G", retaining all other 
dimensions. Compute the resisting moment. 


Number of Ribs. The number of ribs to be used can be as 
indicated by the bases shown in Fig. 151. Therefore, 12 ribs are 
used for the case illustrated above. The thickness of the rib 
should be not less than 1 inch and about tV the clear height be¬ 
tween the bottom and top plates. Also there must be enough 
section in the ribs and hub just below the top plate to take the whole 
load at 10,000 pounds per square inch. In this case the clear height 
is 13 inches, which indicates 1-inch ribs. This thickness gives 
ample section for compression. 

Shape of Pedestal. Cast-iron pedestals may be made round 
instead of square if so desired, Fig. 151. The round pedestal has 
some advantages in manufacture and is especially well suited for 
round piers. The bending moment on a round base is approxi¬ 
mately the total column load multiplied by 0.10 of the diameter of 
the plate. The resisting moment of the pedestal is computed by 
the method given above. 



224 


STEEL CONSTRUCTION 


When a rim is used around the edge of the bottom plate, it can 
be computed in the section resisting bending. This rim is desirable 
in large pedestals. 

There must always be a grout hole at or near the center of the 
pedestal. In large plates additional holes are used. 

Steel Grillage. If the masonry bearing is long and narrow, steel 
I-beams may be used for spreading the load. When so used, they 
are designed in the same manner as given for bearings for beams, 
p. 133. These beams rest directly on the masonry, and are filled 



with cement, concrete, or grout. The webs of the beams must be 
investigated for shearing strength a*nd, if at all deficient, tight- 
fitting separators must be used. Separators should be used in any 
case to hold the beams in position. 

The flanges of I-beams are not always exactly at right angles 
to the webs, hence the beams may not furnish a flat surface for 
seating the columns. This makes it necessary to plane enough off 
the top of beams to provide a true surface for the bottom of the 
column to rest upon. In order to be effective, this must be done 
after the beams are assembled and rigidly held together. 



















































































































































STEEL CONSTRUCTION 


225 


The load from the column must be properly distributed to the 
beams forming the grillage, using a steel or cast-iron plate of proper 
thickness. It may be necessary in some cases to use a cast-iron 
pedestal on the steel grillage. Fig. 153 shows a steel grillage designed 
for the base of a column of a 16-story building. 

CAST-IRON COLUMNS 

Cast-iron columns formerly were used extensively for building 
work, even for fireproof buildings ten or more stories in height. 
Now they are used only for small buildings of non-fireproof con¬ 
struction. The change has come about through greater demand for 
safety and the reduction in cost of steel columns. 

Characteristics. Advantages. The advantages of cast-iron col¬ 
umns are: They offer greater resistance to fire than unprotected 
steel columns. They generally can be more quickly obtained. 
They can be made of any desired shape and ornamented to suit 
the requirements of architectural design. They occupy a minimum 
of space in the building. 

Disadvantages. Cast-iron columns have the following disad¬ 
vantages: For supporting a given load a cast-iron column costs more 
than a steel column. They are subject to defects that are difficult 
to discover by usual methods of inspection. 

Cast-iron columns are made to order. As the brackets and 
flanges must be cast on the column shaft at the time it is made, it 
is not possible to have the column shafts in stock. 

Cast iron is subject to considerable variation in quality, depend¬ 
ing upon the materials used in the melt and the treatment in the 
furnace and in the molds. It may be soft and tough, or hard and 
brittle. It is made in small foundries, as compared with the rolling 
mills which make structural steel. Hence it is not possible to 
control the quality closely, as can be done with steel. 

Blow holes in castings are spaces which the iron does not fill, 
due to bubbles of air or gas becoming entrapped in the mold. Sand 
pockets may be formed by the dropping of sand from the molds. 
In both of these cases the surface of the casting may be perfect, and 
the defects thus difficult or impossible to find. 

The most frequent fault with round columns is eccentricity, 
due to displacement of the core. The core may sag in the mold, due 


226 


STEEL CONSTRUCTION 


to its weight, or it may float in the liquid iron. The result is shown 
in Fig. 154. It may occur at any place in the length of the column. 

At the ends the fault is easily detected, but at 
intermediate points it is necessary to drill test 
holes as indicated in the figure. The test holes 
' should be drilled in the top or in the bottom of 
the casting in reference to its position in the 
mold. An eccentricity of g inch causes appre¬ 
ciable loss of strength. A greater amount than 

Fig Ca\ 5 t 4 dronC?iumn tri0 this sh ° uld C£lUSe ejection. 

Column Sections. Unless there is some rea¬ 
son for using a special shape, cast-iron columns are made round. The 
size is designated by the external diameter and the thickness of metal. 
The sizes commonly made for structural purposes vary from 6 inches 
to 15 inches in diameter and from f inch to 2\ inches in thickness. 

Special sections sometimes used are shown in Fig. 155. The 
angles, U-shapes, and square sections are used chiefly for store front 
work. They are generally made with the exposed surfaces paneled 
or otherwise ornamented. 

H-shaped columns may be used for general purposes. They are 
not as economical as round columns, hence are not much used. In 
some respects they are better than round columns as connections 




Fig. 155. Typical Cast-Iron Column Sections 


are easily made and all surfaces are open to inspection, making it 
easier to find defects. 

Method of Design. The method of designing cast-iron columns 
is similar to that used in designing steel columns. The direct load 
and the concentric equivalent of eccentric loads, if any, are com¬ 
puted in the same manner. The allowable unit stress is computed 
from a formula similar to that for steel columns. The formula 
given under Unit Stresses, p. 51, is 

P= 10,000-60 - 

r 





























STEEL CONSTRUCTION 


227 


Eccentric Loading. The concentric equivalent for eccentric 
!oads is computed by the same formula as used for steel columns, 
viz: 


W' e = W —r 
r 

For round cast-iron columns an approximate formula is 


W 


f 

e 



in which M is the eccentric moment in inch-pounds and d is the 
diameter of the column in inches. 

Fig. 156 shows two cases of eccentric loading of a round column. 
For the load m, the eccentricity e m is the distance from the center of 
the column to the center of the web of the beam. For the load n, 


a 



t 


Fig. 156. Diagrams Showing Eccentric Loading on a Round Column 

the eccentricity e n is the distance from the center of the column to the 
center of bearing on the bracket, this center of bearing being taken at 
2 inches from the face of the column, when standard brackets are used. 

On page 177, it was pointed out that when two eccentric loads 
act about the axis 1-1 and 2-2, respectively, their results must be 
added together. This is true also of rectangular and round cast- 
iron columns. But for round columns the maximum effect of two 
such loads is somewhat less than the sum of their separate effects. 
The resultant varies with the relative amounts of the eccentric 
moments, but the difference is not great and the sum of the separate 
effects can be used without much error. 

Factors Required. If the concentric equivalent load is used, 
the only properties of the section required are: area A; radius of 


































228 


STEEL CONSTRUCTION 


gyration r; and distance to extreme fiber c. The values of these prop¬ 
erties can be computed for the rectangular sections by the methods 
given. For round columns the area is computed from the formula 

A^{d'-d?) 

the radius of gyration is computed from the formula 

f = }V<p+rf 1 > 

the distance c is \ d. In these formulas tv is 3.1416; d is outside 
diameter of column; and d x is inside diameter of column. The 
inside diameter equals the outside diameter less twice the thickness 
of metal. Thus a column 8 inches in diameter and \\ inches thick¬ 
ness of metal has an inside diameter of 5 inches. 

Illustrative Example. Assume a column with the following 
dimensions and loads, and determine the thickness of metal required: 
Length of column 140" 

Concentric load from column above 160,000# 

Eccentric load 40,000#— eccentricity 7" 

Outside diameter of column (assumed) 10" 

Then the eccentric moment is 40,000x7 = 280,000 in.-lb. which by 
the rule on p. 175, is reduced to f X 280,000 = 210,000 in.-lb. 

The concentric equivalent is 

w\ = = 5X210,000 = 105 # 

d 10 

The total load for which the column must be designed is 
Load from upper column 160,000# 

Eccentric load 40,000 

Concentric equivalent load 105,000 

305,000# 

It is now necessary to assume a trial thickness of metal and compute 
the strength. Assume 2 inches. 

A = - (d 2 - d, 2 ) = X (100 - 36) = 50.26 sq. in. 

r = \ = 1 Vl00+36 = 2.9 

P = 10,000 — 60 - = 10,000 — 60X^^ = 7100# per sq. in. 

t z. y 

.*. Total capacity 7100x50.26 = 356,800# 









TABLE IX 

SAFE LOADS FOR ROUND CAST-IRON COLUMNS 
Thousand Pound Units 

,P=10,000 - 60 — 


Values to right of heavy line are beyond limit of length, 70 r. 


Outside 

Diam. 

in. 

Thickness 

in. 

LENGTH 

FEET 

Weight lbs. per 

ft. of length 

a 

a>.- 

Moment of 

Inertia 

1 

Radius of _ 

Gyration » 

6 

8 | 10 

12 | 14 

16 

18 | 20 

22 

6 

§ 

81.7 

73.7 

65.7 

57.8 





33.2 

10.6 

38.6 

1.91 

A 

4 

95.1 

85.6 

76.1 

66.6 



1 


38.6 

12.4 

43.5 

1.87 

i 

107.8 

96.8 

85.8 

74.7 






44.0 

14.1 

47.6 

1.84 

1 

119.4 

106.8 

94.3 

81.7 






49.0 

15.7 

51.0 

1.80 

4 

130.2 

116.2 

102.2 

88.2 






53.8 

17.2 

53 . 9 | 1.77 

Ji. 

140.2 

124.8 

109.4 

93.9 






58.2 

18.6 

56 . 2 | 1.74 

7 

J 

118.7 

109.2 

99.7 

90.2 

80.7 





46.0 

14.7 

72 . 912.23 

i 

135.2 

124.1 

113.0 

102.0 

90.9 





52.6 

16.8 

80 . 6 | 2.19 

l 

150.6 

138.0 

125.4 

112.7 

100.1 





58 . l ) 

18.8 

87 . 212.15 

4 

165.1 

151.0 

136.8 

122.6 

10 S .4 





64.8 

20.8 

92 . 9 ! 2.11 

4 

178.9 

163.3 

147.6 

132.0 

116.4 



1 

1 

70.7 

22.6 

97 . 7 1 2.08 

4 

191.8 

174.7 

157.6 

140.6 

123.5 



1 

76.1 

24.3 

im . 8 ' 2.05 

4 

203 . 8 ' 185.3 

166.8 

148.3 

129.8 

1 

1 

81.1 

25.9 

105.3 

2.02 

8 

* 

142 . 21132.7 

123.2 

113.6 

104.0 

94.61 



53.31 17.1 

113.4 

2.58 

1 

162 . 6 | 151.4 

140.3 

129.2 

118.1 

107 . 0 | 



61.3 

19.6 

126.2 

2.54 

i 

181 . 9 | 169.2 

156 . 6 | 143.9 

131.2 

118 . 6 | 



' 68.6 

22.0 

137.4 

2.50 

4 

200 . 3 | 186.1 

171 . 91157.7 

143.4 

129 . 2 | 



76.1 

24.3 

147.4 

2.46 

4 

218 . 0 ' 202.3 

186 . 6 | 170.9 

155.2 

139 . 5 | 



82.7 

26.5 

156.1 

2.43 

4 

234 . 4 | 217.2 

199.9 

182.7 

165.3 

148 . 2 | 



89.3 

28.6 

163.8 

2.39 

4 

250 . 31231.6 

212.9 

194.2 

175.5 

156.8 


1 

94.8 

30.6 

170.4 

2.36 

9 



156.3 

146.6 

137.1 

127.5 

118.0 

108 . 4 ! 


60.6 

19.4 

166.8 

2.93 

i 


178.8 

167.7 

156.6 1 145.4 

134.3 

123.2 



69 .S 

22.3 

186.4 

2.89 

l 


200.5 

187.8 

175.1 j 162.4 

149.7 

137.0 



78.41 25.1 

204 . 2 ! 2.85 

4 


2 ^ 1.3 

207.0 

192 . 81178.5 

164.2 

150.0 



87.0 

27.8 

220.2 

2.81 

4 


241.3 

225.5 

209 . 81194.0 

178.2 

162.5 



94.9 

30.4 

234.5 

2.78 

4 


260.1 

242 . 81225 . 61208.3 

191.0 

173.7 



103.0 

32.9 

247.3 

2.74 

4 


278.0 

259 . 21240 . 31221.5 

202.6 

183.8 



110.3 

35.3 

258.4 

2.70 

10 



179.7 

170..1 

160 . 5 | 151.0 

141.4 

131.8 

122.3 


68.2 

21.8 

234.6 

3.28 

i 


231.8 

219.1 

206 . 41193.7 

181.0 

168.2 

155.5 


88.2 

28.3 

289.9 

3.20 

4 


280.4 

264.6 

248.8 

233.0 

216.3 

201.3 

185.5 


107.2 

34.4 

335 . 6 | 3.13 

4 


324.9 

306.0 

287.1 

268.2 

249.3 

230.4 

211.5 


125.0 

40.0 

373 . 113.05 

4 


365.9 

344.0 

322.1 

300 . 21278.3 

256.4 

234.4 


141.7 

45.4 

403 . 2 | 2.98 

11 

i 


263.2 

250.4 

237.7 

225 . 01212 . 21199.5 

186.7 

174.0 

98.0 

31.4 

396 . 7 | 3.55 

4 


319.4 

303.6 

287.7 

271.81 255 . 91239.9 

224.0 

208.1 

119 . 5 | 38.3 

462 . 613.48 

4 


371.8 

352 . 9 | 333.9 

315 . 0 | 296 . 0 | 277.0 

258 . 11239.1 

139 . 7 | 44.8 

517 . 8 | 3.40 

if 


420.6 

398 . 6 | 376.6 

354 . 61332 . 61310.6 

288 . 7 | 266.7 

158 . 7 | 50.91 563 . 5 | 3.33 

2 


465.6 

440 . 6 | 415.6 

390 . 61365 . 61340.7 

315 . 71290.7 

176.41 56 . 5 | 601 . 0 | 3.26 

12 

1 


294.7 

281 . 9 | 269.2 

256 . 5 | 243 . 81231.0 

218 . 3 | 204.7 

107 . 5 | 34.61 527 . 1 | 3.91 

4 


358.7 

342 . 81326 . 91311 . 01295 . 21279.3 

263 . 41247 . 1 - 

131 . 4 | 42 . 2 | 618 . 2 j 3.83 

4 


418.8 

399 . 8 | 380 . 8 | 361 . 8 | 342 . 8 ) 323.8 

304.8 

285.8 

320.9 

154.11 49 . 5 | 696 . 0 | 3.75 

4 


475.3 

453 . 31431.2 j 409.2 j 387 . 11365.1 

34 . 3.0 

175 . 5 | 56,4 j 761 . 8 | 3.68 

2 


528.1 

503.0 j 478 . 0 ! 452 . 91427 . 81402.8 

377 . 71352.6 

195 . 8 ! 62 . 8 | 817 . 0 | 3.61 


1 


326.0 

313 . 31300.5 j 287.81 275.0 j 262.3 

249 . 61236.8 

117 . 5 | 37 . 7 | 683 . 5 | 4.26 

4 


397.8 

381 . 91366 . 01350 . 21334 . 21318.4 

302 . 5 | 286.6 

143 . 9 ' 46.11 805 . 314.18 

13 

4 


465.8 

446 . 81427 . 71408 . 71389.7 j 370.6 

351 . 6 | 332.6 

169 . 0 | 54 . 2 | 911 . 314.10 


4 


529.8 

507.7 j 485 . 51463 . 41441 . 21419.1 

397 . 0 | 374.8 

192 . 9 ! 61 . 9 ! 1002.4 4.02 


2 


590.4 

565.21 540 . 01514.81 489 . 61464.4 

439.2 j 414.0 

215.6 69.1 j 1080 . 2 | 3.95 


Make allowance for eccentricity in accordance with the following formula: W e '=5 ~j 

FV e '=EquivaIent concentric load, lb.; il/=Moment of eccentricity, in.-lb.; and d= Diameter,, 
in. See pp. 227, 228. 


























































































































230 


STEEL CONSTRUCTION 


This amount is greater than required, so the thickhess may be reduced. 
It can be shown that the thickness required is If inches. 

Problem 

From the data given above, determine the thickness required for a column 
12 inches in diameter. Note that eccentricity is 8 inches for this diameter 

Tables. The published tables of strength of cast-iron columns 
vary greatly, due to the variety of formulas used. Columns other 
than round are used so little and when used are so likely to be of 
special dimensions that tables of strength would be of little value. 
Table IX gives the strength of round columns in accordance with 
the formula adopted. It also gives the value of r for use in comput¬ 
ing the concentric equivalent for eccentric loads. The Chicago 
Building Ordinance from which this formula is taken limits the 



length of cast-iron columns to 70 Xr. This limit is marked by the 
heavy zigzag line in the table. 

Illustrative Example. Determine the column required to sup¬ 
port a load of 191,000 pounds, the length being 11 feet. 

From Table IX either of the following sizes may be used: 

8" diam. Xlf" metal 
9" diam. X1 metal 
10" diam. Xl " metal 

The 9-inch column is the lightest and will be used if no special con¬ 
sideration indicates the use of one of the other sizes. 

































































STEEL CONSTRUCTION 


231 


Problem 

The loads and lengths of a stack of cast-iron columns are given below. 
Determine the sections. 

4th story, column load, 20,000# length 13 ft. 

3rd. 70,000# length 12 ft.. 

2nd “ “ * “ 115,000# length 14 ft. 

1st “ “ < “ 155,000# length 16 ft 

Basement “ “ 205,000# length 9 ft 



Fig. 159. American Bridge Company Standard Beam Connections 














































































































































































232 


STEEL CONSTRUCTION 


Details of Construction. Splices. Splices in cast-iron columns 
are made by means of flanges as shown in Fig. 157. The load is 
transmitted from upper to lower column by bearing. The bearing 
surfaces must be milled exactly at right angles to the axis of the 
column. If the sections do not match, the metal must be thickened 
as shown at m and n to provide the bearing. Some manufacturers 
set the flanges back from the ends of the column to reduce the area 



of the milled surface. The flange is made wide enough to take a 
row of 1-inch bolts. Four or more bolts are used. 

The splice can be made by means of a dowel plate. It is not so 
satisfactory as the flange splice. It is used when there is no space avail¬ 
able for the flanges, and also for replacing broken flanges, Fig. 158. 

Beam Connections. Beam connections are made by means of 
brackets and lugs cast on the column. The standard connections 
designed and used by the American Bridge Company are given in 
Fig. 159. The entire load is supported by the bracket. The seat 











































































































STEEL CONSTRUCTION 


233 


of the bracket slopes so that the beam will not bear on the end 
of the bracket when it deflects. The lug serves to tie the construc¬ 
tion together and to hold the beam 
upright. Bolts must be us6d for all 
connections to cast iron, as the casting 
would be broken by driving rivets. 

When double beams are used, the 
connection is modified as shown in Fig. 
160. This figure also shows brackets 
for supporting wood beams. Fig. 161 



Fig. 161. Top of Cast-Iron Col¬ 
umn for Supporting I-Beams 



shows the detail of the top of a cast-iron column which supports 
two steel beams. 

Bases. Cast-iron base plates or cast-iron pedestals are used 
for cast-iron columns. They are designed in the manner described 
for the bases of steel columns. If the plate is used, a raised cross 
is cast on the top to fit inside the column and hold it in place, Fig. 
162. If the pedestal is used, the top of it is made to match the 
flange cast on the column. 


TENSION MEMBERS 

Definition and Theory. In building construction, it does not 
often occur that loads must be supported by tension members. 
Occasional special featutes, such as balconies or stair landings, 
require this form of support. The most frequent use of it occurs 
in trusses (which are not covered in this work). 

Axial Tension. A member is subjected to axial tension when 
the load is applied in line with the axis of the member in a way that 
tends .to stretch or pull the member apart, Fig. 163. 




































234 


STEEL CONSTRUCTION 


The strength of steel in axial tension varies directly in proportion 
to the net cross-section area, not being affected by the length (except 
as to the weight of the member) or by the shape of the section. 
Under Unit Stresses, the allowable value of P for axial tension is 
given as 16,000 pounds per square inch; then the strength 
of a section is 

W=P A = 16,000 A 

The area used in this formula must be the net area, i. e., 
the smallest area at any section in the length of the 
member. 

In axial tension the stress is assumed to be distrib¬ 
uted over the entire area, as indicated in Fig. 163. This 
differs from the tension due to bending, which is not 
uniformly distributed but increases from nothing at the 
neutral axis to a maximum at the extreme fiber, as ex¬ 
plained on p. 78. 

Tension Dve to Eccentricity. As in the case of com- 
Fig. 163. Dia- pression members, the load on a tension member may be 
fnga*Tension eccentric, and thus produce both axial tension and ten¬ 
sion due to bending. The discussion of concentric and 
eccentric loads in compression applies to tension members. Fig. 164 
illustrates the stresses from an eccentric load in tension 
which corresponds to Fig. 140 in compression; abed 
represents the total axial tension and a b the axial ten¬ 
sion per square inch due to the load W'; bb' represents 
the tension on the extreme fiber due to the bending 
moment We. Then the total extreme fiber stress due 
to the load W is a b'. The concentric equivalent of 
an eccentric load, as for compression, is expressed by 
the formula 


We'=W'-£ 

r 


4 


m 


If the member is not symmetrical, the value of c to be r- 

, Fig- 164. Diagram 

used is from the neutral axis to the extreme fiber on the 

side toward the eccentric load. in Tension 

Eccentricity in tension members usually results from the form 
of the connection, and in most cases it can be avoided by careful 



















STEEL CONSTRUCTION 


235 


attention to the details. It generally will be more economical thus 
to avoid the eccentricity than to provide the additional section 
necessary to resist it. In altogether too many cases this is neglected. 
The importance of the effect of eccentricity is illustrated by the 
following computations. 

Assume a load of 100,000 pounds concentric, then the net area 

. , . 100,000 „ n _ ' ' • i xt i ii 

required is or 6.25 square inch. Now assume the same load 

with an eccentricity of 1 inch, a value of c equal to 2\ inches and P 
equal to 1.9 inches. The concentric equivalent is 


W’e - = 70,000 # 


The total load is 100,000+70,000 or 170,000 pounds, and the area 
required is or 10.6 square inches. In this case it requires 

JL U jvvV/ 



Fig. 165. Types of Connections for Angles 


an increase of 70 per cent in the section to provide for the eccentricity. 

Fig. 165-a shows a single angle connected by one leg. It is 
eccentric about both axes. Fig. 165-b shows a pair of angles each 
connected by one leg. This is eccentric about the axis 1-1. Fig. 
165-c shows two views of the same pair of angles m, with a pair of 
connection angles n added, which eliminates the eccentricity. 

Sections. Almost any form of steel can be used as a tension 
member. The choice of the section is governed largely by the 
connections that are to be made to it. Of the structural shapes, 
angles, plates, and channels are best adapted for tension members 
in ordinary building work. 

Round rods are used for tie-rods, balcony hangers, temporary 
bracing, and other similar purposes. 











































236 


STEEL CONSTRUCTION 


Eyebars are seldom used in building work, being more especially 
adapted to bridge trusses. They may be used where heavy loads 
occur and rigidity is not important. 


4 \ ► 

< | ► 
< ► 




/K/ w4\ 

< I ► 

*£- 

< l> 

A / , w4v 

7V±r 

< ► 

/ty t , i/ty 






Net Area. Plates and shapes in tension must be connected by 
rivets and the rivet holes must be deducted to determine the net 






























































































































STEEL CONSTRUCTION 


237 


area, of cross section. The number of rivet holes to be deducted in 
any case depends upon their arrangement as explained on p. 69. 
The size of the hole deducted is | inch greater than the nominal 
diameter of the rivet. This allowance is an arbitrary one to cover 
the actual size of the hole, which is about ^ inch larger than the 
rivet, and to compensate for injury to the metal around the hole 
due to punching. Care must be taken to arrange the rivet holes 
so as to retain the greatest possible area at the critical section. 

Round rods can be figured full size if the ends are upset, other¬ 
wise the net area must be taken at the root of the thread. When 
upset ends are used, they are made large enough so that there is an 
excess of strength in the threads, making the whole section of the 
rod available. Generally the threads on rods are cut, but they can 
be made by cold rolling. The latter method makes the diameter at 
the root of the thread somewhat less than the diameter of the body 
of the rod, but the treatment seems to make the steel stronger. 
Tests show that the rolled thread is stronger than the rod on which 
it is rolled, thus making the whole section of the rod available. 

Eyebar heads are always made of sufficient size to develop the 
strength of the bar, so that the whole section is available. 

Details of Connections. Riveted Connections. Riveted con¬ 
nections are required when structural shapes or plates are used. 
Angles, plates, and channels are most commonly used. The top 
connection usually is made with a gusset plate depending from a 
beam or girder. Fig. 166 illustrates a number of such connections. 
The gusset plate may be spliced into the web of a plate girder; set 
in between two channels; may be an extension of the gusset at the 
joint of a truss; or may be connected by angles riveted to the flange 
of an I-beam. (See p. 64). The requirements for the top connec¬ 
tion are that the gusset plate shall be of sufficient thickness to give 
the required bearing for the rivets; and that the rivets connecting 
the plate to the beam or girder, also those connecting the hanger 
to the gusset, be sufficient in number and be placed symmetrically 
about the axis of the tensile stress. 

It has been noted that angles in tension must be connected by 
both legs to avoid eccentricity. This sort of connection is desirable 
for the further purpose of distributing the stress over the entire 
section of the hanger as evenly as possible. Angles in pairs are 


238 


STEEL CONSTRUCTION 


much preferred to single angles. They shduld be stitched together 
with rivets and ring fillers spaced about 2 feet apart. 



Fig. 167. Turnbuckle and Sleeve Nut 


The connections at the bottom of the hanger may be made 
with gusset plates in the same manner as at the top, or the connect¬ 
ing members may be attached direct to the hanger. 




< 

< 

> 

< 

> 

> 







When it is necessary to splice a tension member, it is evident 
that the splice must transmit the entire stress in the member. The 



Fig. 169. Details of End Connection of Eyebnr 


principles involved and methods 
to be used are fully explained 
under Strength of Riveted Joints, 
p. G7, and have been used in 
designing the splices in plate 
girders. 

Details of Rods. Rods are 
specially suited for adjustable 
members. With certain forms of 
connections, the adjustment can 


















































































































STEEL CONSTRUCTION 


239 


be made at the ends; with splices, the adjustment can be made at 
the splice. A rod is spliced by means of a turnbuckle, or sleeve nut, 
Fig. 167. The ends are threaded right and left to make the member 
adjustable. The threaded ends are upset to maintain the full 
strength of the section. The various forms of end connections are 
shown in Fig. 168. They need no explanation. 

Details of Eyebars. Eyebars must be connected at the ends 
with pins, Fig. 169. Refer to “Structural Drafting” for details of 
eyebars. 


WIND BRACING 

GENERAL CONDITIONS 

Horizontal Pressures. In the preceding discussion, the loads 
considered have been gravity loads, i. e., loads acting vertically. 
In addition to these gravity loads, all structures are subjected to 
w T ind loads, or pressures, which are assumed to act horizontally. 
Probably no locality is entirely free from wind storms, so it is always 
necessary to provide for wind pressures in designing the framework 
of buildings. 

It is assumed that wind pressure acts horizontally and bears 
uniformly over the entire windward surface of the building, and that 
it may occur in any direction. These assumptions are not strictly 
correct. The wind may be inclined, due to the contour of the 
ground or to obstructions. It is known that the pressure near the 
top of a building is greater than near the ground; that the pressure 
is not uniform over large areas; that the rush of air around the 
corners produces greater pressure near the corners; and that there 
is a suction on the leew^ard side as well as a pressure on the windward 
side. The wind may strike the building at any angle, but the maxi¬ 
mum effect is produced when it strikes squarely against the side 
(or end) of the building. While the above variations are known to 
be true, it is impossible to provide for them in detail, hence the 
assumption stated above is followed and leads to satisfactory 
results. 

Unit Pressure. Many experiments have been made to estab¬ 
lish the relation between wind velocity and wind pressure. While 
a large amount of data has been developed, the mathematical 


240 


STEEL CONSTRUCTION 


relations are not fully established. Furthermore, it is not certain 
what maximum velocity should be provided for. Hence it is the 
general practice to use an assumed pressure in pounds per square 
foot of the surface. The amount assumed varies. In some cities 
the building ordinances specify the amount to be used; some specify 
20 pounds per square foot; others, 30 pounds. The writer recom¬ 
mends that the framework of all buildings be designed to resist a 
wind pressure of 20 pounds per square foot on the surface of the 
building. It can reasonably be assumed that the partitions and 
walls will add enough to the strength so that the completed struc¬ 
ture will resist a pressure of 30 pounds per square foot. Walls 
should not be counted as resisting any part of the 20 pounds, unless 
practically solid, i. e., without openings. The above recommenda¬ 
tions should be followed with some discretion: increasing the amount 
carried by the framework in very high buildings, and in buildings 
which have few partitions or a very large percentage of openings in 
the walls; decreasing the amount in low buildings, and in buildings 
which have masonry cross walls. In buildings having outside 
bearing walls of masonry and a reasonable amount of cross walls, 
or partitions, these parts may be relied upon to resist the entire 
wind pressure, provided the height of the building is not more than 
twice its width. 

The maximum wind pressure occurs only at long intervals. 
It is, therefore, allowable to use higher unit stresses for wind stresses 
than for gravity stresses. Under Unit Stresses it is provided that 
for stresses produced by wdnd forces alone, or combined with those 
from live and dead loads, the units may be increased fifty per cent 
over those given for live load and dead load stresses; but the section 
shall not be less than required, if wind forces be neglected. Gen¬ 
erally, the members required to support the gravity loads are utilized 
for the wind loads. In such cases no additional area is required on 
account of the wind stress unless this stress exceeds fifty per cent 
of the gravity load stress. 

Paths of Stress. Transmission of Load to Foundation. The 
total wind pressure on the building in the direction under considera¬ 
tion is the assumed unit pressure per square foot multiplied by the 
projected area exposed to the pressure. This pressure must ulti¬ 
mately be resisted by the foundations of the building. Hence, 


STEEL CONSTRUCTION 


241 


£* r 


"4 


I 


a 


to, 


12 , 


f 


SUPPORTED 
15 


By 


there must be paths for transmitting the pressure to the founda¬ 
tions from the area to which it is applied The pressure is applied 
directly to the masonry walls and windows. These are strong 
enough as ordinarily built to carry the load to the floors The floor 
construction, whether of tile arches, concrete, or even wood con¬ 
struction, acting as a horizontal girder, transmits the load to the 
points selected for applying it to the steel framework. Thence the 
steel framework carries the load to the foundation 

Routing the Stress „ The de- , 
signer has some choice as to the 
steel members which he will utilize 
for carrying the wind load So 
far as the steel is concerned the 5| 
shortest path is the best, but other 
considerations may require the 
use of less direct courses, most s, 
commonly through the spandrel 
beams around the outside of the 
building Thus in Fig 170 is 

45 1 

shown a plan of the columns of a 
building, with the typical floor 
framing The heavier lines repre¬ 
sent girders and the lighter lines, /7 i 
joists. 

Considering first the wind 
from either the East or the West, & 
the direction of the load is par¬ 
allel to the narrow way of the 
building and in the same direc¬ 
tion as the floor girders. This 
situation indicates that the wind Fl8 ' ,7 °- F,a 0 f bS for Study 

load should be carried down 

along each E.-W row of columns, viz, 1-4, 5-8, 9-12, etc. Then each 
line of columns and its girders will have to support the wind pressure 
on one panel of the face of the building from top to bottom. It is 
probable that these columns and girders as designed for the gravity 
stresses will carry the wind stresses. (This of course is governed 
by the height of the building.) Now if it were decided to carry the 


14 , 


/a. 


22 , 


26 


COuynrts 
[ 




AHC 


IS, 


25, 


27. 


qri eej 


16 


20 


24 , 


2a, 





















242 


STEEL CONSTRUCTION 


entire load to the two ends and carry it through the columns and 
girders 1-4 and 25-28, the intensity of the stresses would be three 
times as great and probably would require extra metal in these 
members. Therefore, so far as economy of steel is concerned, 
the wind load should be carried down each row of columns. 
But it may happen that, in order to do this, deep brackets are 
required in the lower stories for connecting girders to columns, 
brackets of greater size than is permitted by the architectural 
requirements; then it becomes necessary to carry the load to the 
ends, where the spandrel beams and their connections can be 
made as large as need be A combination of the two arrangements 
may be made, the load above a certain floor being carried down 
on each row of columns, and that below being carried down the 
end rows. 

Next considering the wind from the North or the South, its 
direction is parallel to the joists. It is probable that these joists 
are not strong enough to take the wind stresses without adding 
metal to that required for the gravity stresses. The wind pressure 
can easily be carried to the two sides of the building along the lines 
1-25 and 4-28, where the necessary strength in the spandrel girders 
can readily be obtained. 

The foregoing illustration is comparatively simple; most cases 
are not so easy to settle. In general terms, the designer should take 
all possible advantage of interior framing, carrying through the 
spandrels only that portion of the wind load which cannot be taken 
by the interior framing. 

The bracing strength of the interior framing is limited by the 
strength of the connections to the columns and not by the strength 
of the girder and joist sections. The maximum bending moments 
occur at these connections, and to develop the full strength of the 
beams would require larger brackets than the architectural treat¬ 
ment would permit. So generally it will be that a large proportion 
of the wind load must go through the spandrel beams where the 
limitations as to depth of beams and size of brackets are not so 
restricted. 

It is sometimes possible to use diagonal members for bracing. 
They make the most direct and efficient form of bracing, and should 
be used when the conditions permit. 


STEEL CONSTRUCTION 243 

SYSTEMS OF FRAMEWORK 

A horizontal load can be transmitted vertically by means of 
framework by two systems: (1) by triangular framework, Fig. 171, 


Fig. 171. Diagram of Triangular Framing. 




Fig. 172. Diagram of Rectangular Framing 


having axial stresses; and (2) by rectangular framework, Fig. 172, 
having bending stresses. 

Triangular Framework. Single Panels. Fig. 173 shows a 
single panel of triangular framing supporting the horizontal force IF. 
The reactions at the foundations are R, V', and F. 


R = W 


o*W 


V = V' = 


IF H 


By inspection it is to be seen 
that the stress in a equals IF; in 
c equals V. The stresses in b 
and c can be determined from 
that in a by resolution of forces 
(See Concurrent Forces 



in 


Fig. 173. Diagram of Stresses in Triangular 
Framing 


‘Statics”), as indicated in the figure. These stresses are all axial; 
a and c in compression; b in tension. 

When the values of //, L, and IF are known, the numerical 
values for a, b, c, and V can be determined. 

Two or More Horizontal Panels. Two or more adjacent panels 
can be used, as shown in Fig. 174. It is first necessary to divide 
the load between the two panels. It is simplest to divide the load 
equally, irrespective of whether the panels are equal in length. 





















244 


STEEL CONSTRUCTION 


On this.basis the stress in a equals W, and in d equals \ W. By- 


resolution, the stresses in b and c, 
V l equals the stress in c, V 3 
equals the stress in f, and V 2 is 
the difference in stresses c and /. 
If in this case L t equals L 2 , then 
the stress in b equals stress in e; 
the stress in c equals the stress 
in /; V i equals V 3 ; and V 2 
equals 0. 


and in e and / can be determined. 


vV a d 




Fig. 175. Diagram of Vertical Panels of 
Triangular Framing 


Fig. 174. 


Diagram of Two Horizontal Panels 
of Triangular Framing 


Problem 

Assume four panels similar to those 
shown in Fig. 174. Let H equal 16 feet; 
L,, L 2 , L 3 , and L, equal 20 feet; and IF 
equal 36,000 pounds. Compute the stresses 
in the diagonals. 

Two or More Vertical Panels. 
Two or more panels may be placed 
one above the other as in Fig. 175. 
In this case R t = W 4 + JV 3 +W 2 . 
The value of V l = V 2 is determined 
by taking moments about 0 from 
which 

V — ^2^1 I . 

2 L + ~L + 

W a UI x +H 2 + II 3 ) 

L 

The stresses in the members a to 
k inclusive can be determined by 
the methods given in “Statics”, 
when the values of W v W 3 , W 2 , 
H 3 , II 2 , H v and L are known and 
of R t and V, are computed. 






















STEEL CONSTRUCTION 


245 


Problem 

In Fig. 175 assume W 4 equals 10,000 pounds; W 3 equals 10,000 pounds; 
W 2 equals 12,000 pounds; //, equals 18 feet; H 2 equals 13 feet; H 3 equals 13 feet; 
L equals 16 feet. Determine the stresses in a to k inclusive. 

Extension of Triangular Framework. Similarly, the triangular 
framework can be extended indefinitely in both directions, as in 
Fig. 176. For convenience in solving this case the figure can be 
separated into horizontal tiers, or stories, and each computed. In 
doing this, the anti-reactions of one tier must be applied as loads 



Fig. 176. Diagram of Triangular Framing Extending Over a Building 


in the next lower tier. The horizontal load to be resisted at any 
tier is the sum of all the horizontal loads above that tier; 
thus the horizontal load or shear at the top of the first story is 

w R +w 4 +w,+w r 

Problem 

Assume loads and dimensions for Fig. 176 and compute the stresses in 
the diagonal members. 



















246 


STEEL CONSTRUCTION 


In Figs. 173 to 176 inclusive the diagonals are shown in one 
direction only. As the wind may come from either direction, both 


w 




m 






a: 




x > / 

r\ r\ 

Fig. 177. Diagram of Rectangular Frame 
with Hinged Joints 


W 




T 

'I I 


/|\ /\ 


Fig. 178. Diagram of Rectangular 
Frame with Rigid Joints 


diagonals will be used in all cases. In certain panels, circumstan¬ 
ces may prevent the use of any diagonal bracing, Fig. 176, in 



Fig. 179. Diagram of Rectangular Frame Showing Points of Contraflexure 


which case the stresses must be distributed among the other panels. 

Rectangular Framework. Single Panel. A single panel of 
rectangular framing is illustrated in Fig. 177. The four corners 





























































STEEL CONSTRUCTION 


247 


are represented as being binged, so when the load IV is applied the 
frame will collapse, as indicated by the dotted lines. It has no 
strength to resist the horizontal force. 

Next consider the rectangular frame as shown in Fig. 178. 
The corners are rigidly connected. When the load W is applied, 
the frame tends to take the shape indicated by the dotted lines. In 
doing so, each of the members must bend into reverse curves. Thus 
the frame offers great resistance to the horizontal force. 

When a member is bent into reverse curves, the point of reversal 
is called the “point of contraflexure”. There is no bending stress 
in the member at this point and hinged joints might be introduced 
at such points without affecting the stability of the frame so far as 
the horizontal load is concerned. This is indicated in Fig. 179. 
The point of contraflexure is taken at the middle of the length of 
each member. This is not exactly correct, but is accurate enough 
for designing, in all ordinary cases. 

In order to more easily understand the stresses in the frame, 
consider the points of contraflexure e, /, and g as hinged joints. 
They divide the frame into four parts which can be considered 
separately in determining the stresses. Take first e af, and assume 
the horizontal reactions at e and / to be equal, hence each is \\V. 
The vertical reactions at e and / must form a couple which will 
balance the moment of the horizontal loads, hence, taking moments 
about e, 

VX\L = hWxhU 

from which V = \ W 

The bending moment at a in the vertical member is \Wx\H. 
or \WH\ and in the horizontal member is VX\L which equals 

\W^X\Lot } W1L 

Next consider the part e c, which is subjected to the loads \W 
and V applied at e. The reactions at c are the same in amount but 
opposite in direction. To maintain equilibrium, there must be a 
couple to neutralize the moment of the horizontal force at e about 
the center c. This couple is furnished by the foundation which is 


248 


STEEL CONSTRUCTION 


assumed to be ample to resist the bending moment in the post at c, 


which is 



Fig. 180. Moment Diagram of Single Rec¬ 
tangular Panel 


\Wx\B = \ WH 

In like manner the bending 
moments at b and d can be 
shown to be £ W H. Note that 
the numerical value of the bend¬ 
ing moment is the same at the 
four corners of the frame. The 
moment diagram is given in Fig. 
180. 

In addition to the bending 
stresses in the members, there 
are axial stresses, as indicated 
by the forces and reactions illus¬ 
trated : 


in a 6 § W, compression 

H 

in b d V = | W —, compression 

TT 

in a c V = | W , tension 

Lj 


Problem 

Refer to Fig. 179. Assume W equals 10,000 pounds, H equals 16 feet, 
L equals 20 feet. Compute the axial stresses in the three members of the frame. 
Compute the bending moment at a. ■ Construct the moment diagram. 





Two Horizontal Panels. Next consider a framework of two 
panels, i. e., made of three columns and two girders, as in Fig. 181, 










































STEEL CONSTRUCTION 


249 


subjected to a load W. It is necessary to assume the division of 
the horizontal reactions between the foundations 1, 2, and 3. Sev¬ 
eral different methods are used in practice. It is not of much 
importance which is used, if the stresses resulting from the assumed 
divisions are adequately provided for. In this text it is assumed 
that the reactions at the end columns are one-half of those at the 
intermediate columns. Thus the reactions at 1,2, and 3 are j W, 
% IV, and I W, respectively. By reasoning similar to that used for 
the single panel, the maximum bending moments are found to be: 


at the base and top of columns 1 and 3, 
at the base and top of column 2, 
and in the girders to the right of a and b) 
and to the left of b and c, J 


i H-\WII 

a W X \ H = \WH 

A W II 

WII 


In analyzing this case, the frame may be considered as made up of 
two separate panels, each of which carries one-half the load W. 



Then the bending moment at all maximum points is \\V II. But 
' column 2 is common to both, hence its total stresses are the algebraic 
sums of the stresses from the two panels. As the'bending stresses 
are of the same sign, the bending stresses in column 2 are twice 
those in columns 1 and 3; on the other hand the axial stresses in 
column 2 are opposite in sign and tend to neutralize each other. 
The resultant is zero if L, equals L r The moment diagram of this 
case is given in Fig. 182. 

Horizontal Row of Panels. The foregoing method now can be 
applied to a frame of any number of panels The total horizontal 
load or shear is divided by the number of panels. Give one portion 






















250 


STEEL CONSTRUCTION 


to each of the intermediate columns and one-half portion to each 
of the outside columns. Thus in Fig. 183 there are five panels. 

w 



3 kV 


i w 

J w 







/ ^ J 4 S 6 

Fig. 183, Diagram Showing Division of Shear in a Frame of Five Panels 


The shear is distributed thus: ^TF at columns 1 and 6 t and x IF at 
columns 2 , 3 , 3 , and 5 . The bending moments in columns 1 and 6 are: 
IVH; in columns 3 , 4, and 5, IF II ; and in all girders, W H. 

*.u a u sjyj 



Problem 

Assume a frame of 7 panels, supporting a wind load of 115,000 pounds. 
Let H equal 14 feet. Compute the maximum bending moments and draw the 
moment diagram. 

Two-Story Framcivork. Next assume the case illustrated in 
Fig. 184. This shows the framework of a two-story building. The 
points of contraflexure occur at the points indicated by the black 
dots. The loads applied are Wr at the roof and IF 2 at the second 

























STEEL CONSTRUCTION 


251 


floor. The first-story frame serves as a foundation for the second- 
story frame. The horizontal shears which are transmitted through 

the points of contraflexure in the second-story columns are \ W R 
and ^ Wr as indicated; those transmitted through the points of 

contraflexure in the first-story columns are \ (W R +W 2 ) and ^ 

o 3 

as shown. The vertical shears transmitted through 

1 WrH 

points of contraflexure in the roof girders are Vr = - ——and 

6 L 

those transmitted through the second-floor girders are 

ir _1 lift H 2 + (JV R -f- W 2 ) H 1 
2 6 L 

(assuming panels of equal length). Then the bending moments are 


at a in roof girders 
at b in 2nd floor girder 
at c in columns 
at d in columns 
at e in columns 
at / in columns 


-T2 W * H > 

-j \iw r h 2 +(Wk+w,) H ,] 

+h w « H > 

+\w r h, 

+^(.w K +w,) //, 

+~(W R +W t ) II, 
b 


An important relation to be noted is that at any joint the sum of 
the moments in the members equals zero, or the sum of the moments 
in the column equals the sum of the moment in the girders. Thus 
at column 1, 2nd floor 

H,-^IW r H,+(W r +W 1 ) H,\=0 

at column 2, 2nd floor 

i WbH 3 +^(W r +W % ) H,-2X^{W b H 3 +(.W r +W,) h,)=o 




252 


STEEL CONSTRUCTION 


Extension of System in Either Direction. The method can now 
be applied to a frame of any extent, vertically and horizontally. 
Fig. 185 shows such a frame six panels in width and six stories and 
basement in height. The loads applied at the several floor levels 
are represented by W v W 2 . ... W r. The total shears in the 
several stories are represented by Wr, W^, W 2 . W/. 



The total shear in any story is the sum of all the loads applied at the 
floors above, thus, 

W t ' = W,+W 4 +W % +W 9 +W B 

The total shear in any story is divided between the columns in that 
story in accordance with the rule given. This is illustrated in the 
figure by the values given in the first story. 


























STEEL CONSTRUCTION 


253 


The bending moments are illustrated at the third floor in the 
figure and the moments diagrams at the fifth floor. 

The procedure can now be reduced to simple rules and formulas. 

The bending moment in an intermediate column in any story 
equals the total shear in that story multiplied by the story height, and 
the product divided by two times the number of panels. This is 
expressed by the formula 


M = 


W'H 
2 n 


The bending moment in an outside column is one-half that in an 
intermediate column, or, 

W'H 


M = - 


4 n 


The bending moment in a girder is the mean between the bending 
moments in the column above and below the girder. It is expressed by 

the formula 


M 


-K 


Wa'Ha , W b 'H b 


) 


( Wa'Ha + Wb'Hb) 


2 n 2 n J 4n 

Note, a and b refer to two adjacent stories, as the third and fourth. The 
panel length does not affect the value of the bending moment. 

Illustrative Example. Compute the bending moments at the 
first floor in the frame in Fig. 185. Assume that the loads applied 
above the first story sum a total of 66,000 pounds equal Wf, those 
above the basement story a total of 75,000 pounds equal 
Let II b equal 10 feet, and II 1 equal 16 feet. Then the bending 
moment is: 

in an intermediate basement column 

75,000 X10 = 62>5QQ fL _ lb> 

2X6 

in the intermediate first-story columns 

66,000 X J6 = 

2X6 


in the first-floor girders 

M±S8,000 =75(250 ft 4b 

Axial Stresses. The axial stresses may be disregarded in most 
cases. They are usually small in proportion to the sections otherwise 
required for the members. The girders may be considered as being 









254 


STEEL CONSTRUCTION 


relieved from this stress by the floor construction. If there be no floor 
construction along the girders, the axial stress should be considered. 
In the intermediate columns the axial stress is zero if the panel 


Er 

\ 

6 




Et 

5 




W—t 

4 



K 

Er 





E§ 

3 




zzt 






/ 

FIRST 

FLOOR 


< 





\ 

§. 





L 


Fig. 186. Diagram of Overturning Stresses in a Building Frame 

lengths are equal. In the outside columns the axial stress occurs, 
but here the bending moment is only one-half that in the intermedi¬ 
ate columns, so the axial stress is usually not important; however, 
in tall, narrow buildings it may be important and should be com¬ 
puted. When required, it can be computed thus: In Fig. 186 the 
arrows represent the wind pressure on the framework shown. The 





















STEEL CONSTRUCTION 


255 


resultant .of this pressure is IV, acting at mid-height of the exposed 
part of the structure. The axial stress V in the basement section 
of the end column is found by taking moments about the point B. 
The stress in the first-story section is found by taking moments 
about the point 1. 

Problems 

1. Assign values to the structure illustrated in Fig. 186 and compute the 
axial stress in the second-story sections of the end columns. 

2. In Fig. 185 assume the following values: 

h b = io'-o' 

H, = 16'-6' 

H 2 , H 3 ---H a = 12-6' 

W x = 8 , 000 # 

W 2 = 14,500# 

W s , W it W 6 , W 6 = 12,500# 

W R = 10 , 000 # 

(a) Compute W B ', IP,', - Wf. 

(b) Compute the maximum bending moment for an interior column 
above and below each floor line. 

(c) Compute the maximum bending moment in the girders at each floor. 

(d) What is the bending moment in the second-floor girder at a point 
1-9' to the right of column 4? 

(e) Construct the moment diagram for column 7 from basement floor to 

roof. 

DESIGN OF WIND-BRACING GIRDERS 

In the preceding pages the method has been developed for 
determining the bending moments in wind-bracing girders and 
columns. It has been shown that the maximum bending moment 
occurs at the intersection of the column and the girder, and zero 
moment occurs at the center of the girder. Between these points 
the moment varies uniformly, as shown by the moment diagrams in 
Figs. 180, 182, and 185. By laying out the moment diagram to 
scale, the bending moment at any point may be measured. 

End Connections for Riveted Girders. Heretofore in designing 
beams, end connections have been required to resist only vertical 
shear, but in the case of wind-bracing girders it is evident that the 
connection of the girders to the column is chiefly to resist the bending 
moment. This connection requires careful designing to insure 
effective results. 

To illustrate the design, assume an example as follows: In 
Fig. 187 the distance center to center of columns is 20 feet; the max- 


































































































































































































































STEEL CONSTRUCTION 


257 


imum bending moment is 400,000 foot-pounds or 4,800,000 inch- 
pounds; the depth of girder is 3 feet % inch back to back of angles. 
As stated on page 51, the unit stresses to be used are fifty per cent 
in excess of those allowed for gravity loads. 

The girder connects to the web of tfie column. As the end of 
the girder thus lacks only about an inch of reaching to the column 
center, the maximum bending moment must be provided for, viz, 
4,800,000 inch-pounds. 

Rivets Connecting Girder to Column. The rivets through the 
end angles and column webs are field driven, f inch diameter, and 
on the tension side of the girder (above the neutral axis in this case) 
are in tension. As in a beam, the unit fiber stress varies from zero 
at the neutral axis to a maximum at the extreme fiber; so the unit 
stress in these rivets varies from zero at the neutral axis to the max¬ 
imum allowable amount at the farthest rivet. 

Then, if the rivets are equally spaced, the average stress is 
one-half the maximum. The total resistance of the rivets is the 
average value of one rivet multiplied by the number of rivets in the 
tension (or compression) group represented by t (and c); the centers 
of gravity of the groups are at the points t and c. The moment arm 
is the distance a between t and c, and the resisting moment is aXt 
(or c).* The number of rivets required is determined by trial. The 
full value of a f-inch rivet, field driven, in tension is one and one- 
half times 6000 pounds or 9000 pounds. Several trials lead to the 
use of 28 rivets on each side of the neutral axis. The value of t is 

9000 X -8 or 226,000 pounds. The moment arm a is 42 inches and 

the resisting moment of the joint is 126,000X42 or 5,292,000 inch- 
pounds, which is about ten per cent in excess of the bending moment. 

Problem 

Design the above joint, using f-inch rivets spaced 2\ inches. 

Rivets Connecting End Angles to Gusset Plate. Now consider the 
rivets connecting the end angles to the gusset plate. The method 
is the same as that for the connections of the end angles to the 
column, except that the rivets are shop driven in double shear. 

*This is not exact, for the rivets on the compression side do not act, the compression being 
resisted by the direct bearing of the end of the girder against the column. The error is on the 
safe side 




258 


STEEL CONSTRUCTION 


The required results can easily be obtained by comparison with 
field-driven rivets. With one row of rivets there will be one-half 
as many (less one). One shop rivet in double shear is good for 
21,660 pounds. This is greater than the value of two rivets in ten¬ 
sion (18,000 pounds), hence the proposed arrangement is satis- 
' factory. It gives greater strength than is required. 

The thickness of gusset plate required to develop the full 
shearing value of the rivets is fg inch. The thickness required for the 
actual stress is ^ inch, which use. (See rivet tables in handbook.) 

Problem 

What thickness of gusset plate is required for f-inch shop rivets? 

Bending Stresses in Connecting Angles. No accurate determi¬ 
nation can be made of bending stresses in connecting angles, so 
thickness must, be adopted arbitrarily. If the gage line of the 
rivets is not more than 2\ inches from the back of the angle, the 
thickness should be f inch. In many cases wide angles with large 
gage distance must be used in order to match the gage lines in the 
column. A thickness of 1 inch seems to be safe for a gage distance 
of 4 inches. Intermediate values may be interpolated. 

Gusset Plate. The slope of the gusset plate should be about 
45 degrees, but may vary to suit conditions, such as clearance 
from windows, etc. Stresses in the gusset plate may be imagined to 
act along the dotted lines shown in the figure. On the tension side 
of the girder the plate is in tension, and on the compression side in 
compression. The thickness of plate required for rivet bearing is 
sufficient to give the necessary strength on the tension side, but on 
the compression side stiffener angles may be required. These 
angles can be designed according to rules similar to those given for 
the stiffeners of plate girder webs, p. 148. They should be used 
when the length of the diagonal edge of the plate is more than 
thirty times the thickness. The leg of the angle against the plate 
should be of suitable width for one row of rivets, say 3 inches, 3£ 
inches, or 4 inches. The outstanding leg may vary from 3 to 6 
inches. A thickness of § inch is suitable usually; it may be made 
more or less to be consistent with size and thickness of the main 
members of girder. For the case illustrated use 2Ls 3|"X3|"X i*. 

Girder Section. The critical section of the main girder is at 
the end of the gusset plate (because there are no gravity loads). The 


STEEL CONSTRUCTION 


259 


gusset plate being 2'-6" wide, the bending moment at this point, as 
determined from the moment diagram, is 300,000 foot-pounds, or 
3,000,000 inch-pounds, Fig. 187. 

It is usually economical to make the girder as deep as condi¬ 
tions will permit. In most cases it is limited by the windows above 
and below. For this case 3'-(H" back to back of angles is assumed. 

The section is determined by the methods given for riveted 
girders, p. 141, using the increased unit stresses previously men¬ 
tioned. Note that the web is spliced at the point under consid¬ 
eration. 

The spacing of rivets that connect the flange angles to the web 
plate is determined as in riveted girders, p. 149. As the bending 
moment varies uniformly from the center to the end, the rivets are 
equally spaced. This, spacing may be continued for connecting 
the flange angles to the gusset plate. But there must be enough 
rivets through the gusset plate to transmit all of the stress which 
is in the flange angles at the edge of the 
gusset. Connecting angles may be needed 
to assist in connecting the flange angles 
to the gusset plate. 

Problems 

1. Design the girder section, flange rivet¬ 
ing, and web splice, Fig. 187. 

2. Make drawing at 1-inch scale showing 
side elevation, end elevation, and section of the 
girder. (Use the design with f-inch rivets.) Show 
rivet spacing. 



Fig. 188 Section of Connection 
of Girder to Column 


Other Forms of End Connections. Fig. 188 shows a girder con¬ 
nection differing from the previous case in that the column is turned 
in the other direction. The connection is designed in just the same 
manner but the amount of the bending moment is somewhat less 
than the maximum because it is some distance away from the center 
of the column. The actual amount can be computed or scaled from 
the moment diagram. 

Problem 

What is the bending moment at the end of the girder shown in Fig. 188, 
the moment at the center of the column being 400,000 foot-pounds and the 
distance, center to center of columns, 16 feet? 

In Fig. 189 the web of the girder connects directly to the flange 
of the column. This form of connection is suitable for girders which 









260 


STEEL CONSTRUCTION 


are deep in proportion to the bending moment which they must 
resist. The method of designing the connection is the same as that 
explained for Fig. 187, except that the rivets are in single shear in¬ 
stead of tension, and that the rivets are not evenly spaced, hence 
the average resistance may not be one-half the maximum. The 
value of each rivet can be measured from the diagram at m in the 




Fig. 189. Details of Connection of Girder Directly to the Face of the Column 

figure. Having the values of the several rivets, the center of gravity 
of each group, i. e., the positions of the resultants t and c, can be 
found in the usual way. 

Problem 

Compute the resisting moment of the connection shown in Fig. 189. Use 
1-inch rivets, and assign suitable spacing for them. Design the girder section 
cortesponding to this resisting moment. , 

When the form of connection shown in Fig. 189 is not ade¬ 
quate, the gusset plate can be used connecting directly to the flange 
of the column. It involves no principles or methods different from 
those already explained. 





































































STEEL CONSTRUCTION 


261 


End Connections for I =Beam Girders. I-beam connections for 

resisting bending are illustrated in Figs. 190, 191, and 192. 



Fig. 190. Connection of I-Beam to Flange 
of Column For Wind Bracing 




Fig. 191. Connection of I-Beam to Side of 
Column for Wind Bracing 



The detail in Fig. 190 is 
simil ar to the connection shown 
in Fig. 189. It can develop 
only a small part of the capa¬ 
city of the beam. 

The detail in Fig. 191 also 
can develop only a part of the 
capacity of the beam, but it is 
available for making use of the 
floor girders in the upper part 
of the building for resisting 
wind stresses. The strength 
of this connection is limited 
by the bending resistance of 
the connecting angles or the 
strength of the rivets. 

Problem 

Compute the bending resist¬ 
ance of the connection shown in 
Fig. 191. 

Bracket Connection. The 
connection in Fig. 192 can be 
made to develop the entire net 
bending resistance of the beam 










































































































262 


STEEL CONSTRUCTION 


(deducting for rivet holes in the flanges). The connection of the 
brackets ±o the column is designed jn the same manner as described 
for the gusset plate connection. The average value of the rivets is 
determined from the diagram as at m. Fig. 189. In the connection of 
the brackets to the beam, all the rivets are figured at the maximum 
value. Their resisting moment is their total shear value multiplied 
by the depth of the beam. 

Problem 

Design a bracket connection that will develop the net bending resistance 
of a 24" I 80#. 

COMBINED WIND AND GRAVITY STRESSES IN GIRDERS 

The girders which are usually used to resist wind stresses are 
also subjected to gravity stresses in supporting walls and floors. 
It is necessary, therefore, to determine the combined effect before 
the member can be designed. 

Moment Diagram for a Restrained Beam. In the discussion of 
beams, it was considered that the ends rested freely on the supports. 

With these conditions the beam 
under a gravity load tends to 
deflect in the form of a simple 
curve and its moment diagram 
lies entirely below the axis o-o, 
Fig. 193-a. If the beam is re¬ 
strained by rigid connections at 
the ends, as illustrated in Fig. 
192, it tends to deflect in the 
form of a compound curve and 
the moment diagram, Fig.l93-b, 
lies both above and below the 
axis.. The part of the diagram 
above the axis represents nega¬ 
tive moment and the part below, 
positive moment. The total depth of the moment diagram is l W L 
(for a uniformly distributed load) in each case. 

Positive and Negative Moments. The division of the moment 
diagram of a restrained beam between positive and negative moments 
depends on a number of conditions. The conditions usually assumed 
as ideal are that the beam is of constant cross section from end to 








































































































































































STEEL CONSTRUCTION 


263 


end and that the end connections are absolutely rigid. Then the 
bending moment at the ends is —jz W L, and at the middle is 

+k WL - 


If the section of the beam at mid-span is less than at the ends, 
as is the case when the connections are made by deep gusset plates 
or brackets, the positive moment is less and the negative moment 
greater than the above values. The extreme case would be when a 
beam had no bending resistance at the center (as if hinged), in which 
case the two halves would act as cantilevers; there would be no 
positive moment and the negative moment would equal \W L 
(W being the total load on the span). 

The assumed ideal condition of absolute rigidity at the ends 
is not realized because the columns must deflect laterally under 
load. This lack of absolute rigidity tends to decrease the negative 
moment and to increase the positive moment. The same effect is 
produced if the connection is not sufficient to develop the strength 
of the beam section, as in the examples shown in Figs. 190 and 191. 
In the extreme case when the columns or the connections are ex¬ 
tremely weak in bending resistance, the negative moment approaches 
zero and the positive moment approaches | W L. 

It is not practicable to determine definitely the amount of 
negative and positive moments for a given case, so arbitrary values 
must be adopted. The designer generally should assume that the 

moments from the gravity loads are — j- WL at the ends and 


-f — WL at mid-span, and should design the end connections and 
24 


the beam section accordingly. But a less value may be used at 
the ends and a corresponding greater value at the center if it is 
not possible to make end connections strong enough to resist the 
larger value. 

Bending Moments for Combined Loads. Now consider the 
bending moments resulting from the combined action of gravity 
and wind loads. In Fig. 194, let a be the moment diagram for a 
wind load and Jb the moment diagram for a gravity load. Then the 
total effect is represented by c, which is the moment diagram for 





























































































































































































































































































































































































































































































































































STEEL CONSTRUCTION 265 

I Wk . ■ V- ' * 

the combined loads. This moment diagram c is constructed by 
adding together the moments used in constructing the diagrams a 
and b. 

End Connections Designed to Resist Wind Loads. Diagram c, 
Fig. 194 shows a very- large resultant negative bending moment at 
the left end of the diagram, and a very small resultant positive 
bending moment at the right end. If the respective end connec¬ 
tions be designed to resist these moments, i. e., the left end with a 
very heavy connection and the right end with a very light connection 
(in this case practically a hinged joint), then the distribution of 
stresses probably would be as represented in diagram c. But, since 
the wind may act from either direction, the two end connections 
are made alike; the columns at the two ends are probably of about 
equal size and stiffness; then it is reasonable to assume that the 
deflections, and hence the resistance developed at the two ends, will 
be equal. 

For this condition it is evident that diagram c does not repre¬ 
sent the actual distribution of moments. To have a diagram which 
will represent it, the curve must be shifted so that the negative 
moment at the left.end equals the positive moment at the right end. 
This gives diagram d. The same diagram results directly by com¬ 
bining diagram a of Fig. 193 with diagram a of Fig. 194. It will be 
noted that the bending moments at the ends equal the bending 
moments from the wind loads. Hence, the end connections in all 
cases are designed to resist the wind load moments. 

Maximum Bending Moment. The bending moment at the 
center of the span equals the bending moment of the gravity load 
computed for an unrestrained beam. However, the maximum posi¬ 
tive bending is not at the center, but some distance to one side (to 
the right in this case) and its amount can be determined by con¬ 
structing the diagram d. The value thus determined governs the cross 
section of the girder. 

As has been stated, the unit stresses allowed for the combined 
loads are 50 per cent larger than those for the gravity load alone. The 
resulting section designed for the maximum positive bending moment 
from diagram d will always be larger than the section required by 
the negative moment of gravity load from diagram b and more than 
twice the section required by the maximum positive bending moment 


26 6 


STEEL CONSTRUCTION 


from diagram b, diagram b being the moment diagram for the gravity 
loads on a restrained beam, when the wind is not acting. Note, 
however, that the section required is less than would be required 
for the gravity load on a simple (unrestrained) beam, diagram a, 
Fig. 193. 

Problems 

1. In Fig. 194 assume values given for diagrams a and b. Determine the 
maximum positive and negative values for diagram d. Construct diagram d 
accurately to scale. 

2. Design a girder of the type shown in Fig. 187 from the moment dia¬ 
gram d in Fig. 194. 

EFFECT OF WIND STRESSES ON COLUMNS 

Combined Direct and Bending Stresses. The bending moment 
on the column due to wind loads produces the same sort of stresses 
as result from the bending moment due to eccentric 
loads or any other cause producing flexure. The ex¬ 
treme fiber stress is computed from the formula 

o Me 

s= T 

This stress is added to the stresses resulting from the 
direct and eccentric loads on the column to give the 
maximum fiber stress. 

The combination of the direct and the bending 
stress is illustrated in Fig. 195. The stress from the 
direct -load is represented by the rectangle abed and 
the unit stress by a b. The stress from bending is rep¬ 
resented by the triangles b b'o and c c'o, the extreme 
fiber stress being b b' in compression and c c' in tension. Then the 
maximum fiber stress is on the compression side and is ab + bb'. 
Thus b b' represents the increase in stress due to the wind load. 
IP, as is usually the case, b b' amounts to less than half ab, the 
column section required for the direct load need not be increased on 
account of the wind stress, because of the increased units allowed 
for combined stress. But if b b' exceeds one-half of a b, the combined 
stress will govern the design using the increased unit stress. 

On the tension side of the column, the wind stress will very 
rarely be great enough to overcome the direct compression. And 



Fig. 195. Dia¬ 
gram of Com¬ 
bined and Di¬ 
rect Stress 


■ 









STEEL CONSTRUCTION 


267 


if there should be a reversal of stress, there cannot be tension enough 
to require any addition to the section. It frequently occurs that 
the wind bracing girder connects to the column in such a position 
that one side of the column must resist practically all the wind 
stress. Such a case is illustrated in Fig. 189. With these condi¬ 
tions only one-half the column section should be used in computing 
the resulting extreme fiber stress. 

Design of Column for Combined Stresses. The procedure in 
designing the column section, when the combined wind and gravity 
loads govern, is the same as has been given for columns with eccen¬ 
tric loads, p. 174. The method there given for computing the con¬ 
centric equivalent load also applies, as well as the formula 


As applied to wind load (refer to Fig. 196) WJ is the equivalent 
concentric load, i. e., the direct 
load that would produce the 
same unit stress; IF'is the hor¬ 
izontal shear which is assumed 
to be carried by the column 
under consideration and is as¬ 
sumed to be applied at the 
point of contraflexure of the 
column (see Fig. 185); e is the 
moment arm expressed in 
inches, hence W'e is the bend¬ 
ing moment in inch-pounds at 
the section under considera¬ 
tion; c is the distance from 
the neutral axis of the column 
to the extreme fiber on the 
compression side; r is the radius of gyration of the column in 
the direction under consideration. The critical section of the 
column is at the top of the bracket, as the bracket has the effect 
of enlarging the column section, so the distance e is measured to 
that point. 

To illustrate the use of the formula assume the following data: 



Fig. 196. Details of a Problem in Wind Bracing 

































268 


STEEL CONSTRUCTION 


Direct or gravity load on column is 600,000 pounds; W is 10,000 
pounds*, e is 30 inches; c is 7 inches; and r is 3.5 inches. Then 

WJ = V °’Hx 3°5 X ^ 7 = m ,4 °° # 

As this is less than half the gravity load it is neglected 

Problem 

In Fig. 196 are given the essential dimensions and the loads on the columns 
in the first and second story of a building and the girders at the second floor. 

(a) Design the columns and girders. 

(b) Write a complete record of all computations. 

(c) Make a drawing of the joint at J-inch scaje. 







FORT DEARBORN HOTEL, CHICAGO 

Holabird & Roche, Architects 















STEEL CONSTRUCTION 

PART IV 


PRACTICAL DESIGN 

SIXTEEN-STORY FIREPROOF HOTEL 

Having studied the stresses and the design of individual steel 
members, attention will now be given to the problems which arise in 
the design of the structural framework of a building. 

It is assumed that the student now understands how to com¬ 
pute stresses and how to design individual members of the frame¬ 
work; therefore, detailed computations of these operations in 
most cases are not given. Nor are references given to the preceding 
parts of the work, except in a few cases, it being left to the student 
to seek these references for himself if he needs them. This applies 
also to the tables and diagrams in this book and in the handbooks. 

Description of Building*. The building selected for the purpose 
of illustrating the practical problems of design has been taken 
because it gives an unusually large number of special conditions. 
For this reason it cannot be considered as a typical case. Its fram¬ 
ing differs from that most commonly seen in buildings because 
steel joists are not used. 

The building is designed to be used as a hotel. It has sixteen 
stories and an attic above street level and a basement below street 
level. It also has a sub-basement over part of the area to provide 
space for a power plant. The basement extends under the sidewalk 
on two sides of the building. 

The building occupies the entire lot, except for a light court 
above the third-floor level. Fireproof construction is used through¬ 
out. The framework consists of structural steel columns and 
girders. The floor construction consists of reinforced concrete 
slabs and joists, with tile fillers between the joists. In most of the 


•The Fort Dearborn Hotel, Chicago, Illinois; Holabird and Roche, Architects. 




270 


STEEL CONSTRUCTION 


building the concrete slabs form the finished floor. Partitions in 
general are three-inch hollow tile, plastered on both sides. They 
are fixed in position (this has some bearing on the arrangement of 
girders). The foundations are cylindrical concrete piers extending 
to rock. The basement walls are of reinforced concrete. The walls 
above grade are brick with terra cotta trimmings. 

Plates A to X give the complete structural framing plans, and 
a part of the architectural floor plans and elevations, which are 
sufficient for this problem; but additional architectural details 
would be required for making the complete design. 



Plate A. Foundation Plan, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 

































































































































/{E3 



Plate B. Basement and Sub-Basement Plans, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 









































































































































































Plate C. First Floor Framing Plan and Details of Beam Connections, Fort Dearborn Hotel 

Courtesy, IJolabird & Roche, Architects 








































































































































































































































/<$ -// ' , !6 S * | 16-s' , /6-S | /6-S 



E36E- FLOOR 


SPANPREL 


CONNECTIONS TO COLUMNS 14-J5 
? clp pi nnR 



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6X4 XjL 


CONNECTION TO COLUMNS6 
p pl On# 



E-5XSXgX /?- 6 L s over fresh 
air intake Cot 3-/5-/ Re cjd. 
E-SXJx/X4 : OU over door 
ope mny. Col 3 S -36 -1 Re fid 



Plate D. Second Floor Framing Plan and Spandrel Connections, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 











































































































































































































-T ftp- FLO Oft FRAMING PLAN. 

Plate E.- Third Floor Framing Plan and Spandrel Sections, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 



































































































































































I 



Courtesy , Holabird & Roche , Architects 













































































































































































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LINTELS OVER OPENINGS 
IN PENT HOUSE WALLS 



Plate G. Roof Framing Plan, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 












































































































































































































Plate H. .Details of Chimney, Columns, and Bases, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 







































































































































































































M/SCCLLANEOUS DETAILS. 

Plate I. Miscellaneous Details, Fort Dearborn Hotel 
Courtesy, Holabird. <fc Roche, Architects 

















































































































































































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Courtesy, Holabird & Roche, Architects 


















































































































































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Courtesy, Holabird & Roche, Architects, 












































































































































































































m 


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-A Xjx£ X S'-0"E?-TP , eq'J 


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L IN TEL -5 OVER OPENINGS 
US PENT HOUSE WALES 





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2-Mu thon fodsj ^ 


High Po>nt of Root TjrH'.j 
L /e v <? A on // 6^, jr 


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SPANDREL COL /-0 
ESS PL OOP. 
,-3.6: ,-} 


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^“Roch 2-6 C-C 
2-A'AJ x£ 1* 
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Wt ton Rods 


a nchor e d >n masonry 
74, 



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"P/f near SSe 

peinporcinc op 
SPANDREL C/PPER 
COL S-/S- 15-22 A 22 29 



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SPANDREL COL , 3 
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,6 la FL OOP 


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2 0° FLOOR 
CONN TO COL 1-7 


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SXj Pi over 
windows — 


SPANDREL FRAMING INTO 
din -a me PCS /NCL 



BPACRET FOR ^ 

MCTAL BALCONIES ATS'SK) 

lis 9is//Es k/3is floors 

i^XA-O-HC.-C Rods 
to be. used where 2/1\ 
S09ndr*U occur . 

r k _n 4li 


I fZ-j ^Million Rod 
• trend at f/oor /me 

/ lo'Xj Pit bttween 
window 




SPANDREL COL l-ZS, 
6-7 t 7 14 t 35-42 
I SEP FLOOR. 


Top 211 
Top IS 'I 
Tip IS "I 
rdc 


SPANDREL 

!6th 


pfiods-2-6~ C-C: 

6 '/z Pit m wmdow 
FlOO' t,l• 

{For 6~P!t. 

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COL 2-6 L !4 -JS 


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'Rods-2-6 C-C forS Pit. 


5 ~X{ Pit ,n wmdow openings ^ 


! p/tM" ; 7 r jf/vi For S P/t. 
\bttnaen nint/kns ' For /C Pit, 

SPA N PR EL COL 1-2 i 6-7 
A 7-14 A 35-42 
/6LH FLOOR. 




POL-15 'ol. 

TjTdzoi ’c ? id Ft 

""7 SPANDREL COL 2-6 A 
JJ V /4-35 

15IS FLOOR 


L 0 CAT I ON OF 
FIRE ESCAPE 


_|_ ctLhss - 

I *i. rOut.Side fate of wall 


CHA NNEL 5 
SUPPORTS 


POP 

■ COD S'/E. 


TYPICAL 5P/JNPPEL PE TP US. 

Plate L. Typical Spandrel Details, Fort Dearborn Hotel 
Courtesy, Holabird <fc Roche, Architects 





































































































































































Plate M Basement and Sub-Basement Plans, Fort Dearborn Hotel 
Courtesy, Holabird &. Roche, Architects 




















































































































































































































































VAHBUBFN jSr. 

't-S -T- /6's . /i'-s 


/ 



F/ej'r Fiaoe pi s)/v 

Plate N. First Floor Plan, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 


t 

































































































































































'6 Xg PLTS - TOP A- BOTTOM 
UPPER SECTION ■COL. 33 


COL 0-12 X^ WEB PLT 
*> l% — [4-6X6 XJ Lj 

^ l FLO OP L INC CoL - LOAO‘ 662, OOO* 



ABOUT IS C-C. G/RDER' 
ADJUST WITH FILLER 
PL A TES. 


4-7X3;xflJ- 


/6 Xg X'J-O PLATE. 


20 X 26 X2- t STEEL SLAB 


30 PI VETS 


PI VETS , 
A-S'xjg'xi & 
GRIND TO fit. 


j'F/LLCPS- 


2 GIRDERS 

EACH 

I-WC8PLJS& 
4-L‘6X6xf 


r- fillers 

4 COVER PLT& 
/4 xj'GRIND 
TO+F/T 


I 


CUT OUTSIDE COVER PLT ON \5 - s'x 3/x ,/ "u 

each flange under c/pder and hull 

COL 34 M-16,4 23.000 INCH POUNDS FOR EACH G/ppER 


REACTION 134,000* FOR 

each Girder. 


Plate O. 


plate girder at at*, floor 


REACTION 201, OOD*FOR 
EACH G/ROER. 


Details of Special Plate Girder at Fourth Floor Showing Offset of Column 33 Fort 

Dearborn Hotel 

Courtesy, Holabird & Roche, Architects 



Courtesy, Holatnrd & Roche. Architects 


■LOWER SECTION COL 33 



















































































































































































































































































/6-Sf /6-j' .1, /«'-/* -| T J6-S -,u !t-f \--4«- 



Plate Q. Third Floor Plan, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 

















































































































































































■9/ ' S-- 9/ s- 9 , /7*/-r -jrjp . ?/ 1 fa 



Plate R. Typical Floor Plan, Fifth to Fourteenth Floors, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 




















































































































































































Ml 

rcr co**<~* 


■eoof-Pi an- 

Plate S. Roof Plan, Including Vertical and Horizonta ISections of Penthouse, Fort Dearborn 

Hotel 

Courtesy, Holabird & Roche, Archilec 































































































































































































TYPICAL 


SPANDREL J. 



Plate T. Sections of Typical Spandrels, Fort Dearborn Hotel 
Courtesy, Holabird & Roche, Architects 
















































































































































































































































/.» 3e St ere r fnc^or. 


Plate U. LaSalle Street Front Elevation, Fort Dearborn Hotel 
Courtesy, Holabird, & Roche, Architects 



















































































































































































































































































































































































































































































































































































































































































Plate V. Alley Elevation, Fort Dearborn Hotel 
Courtesi/i Holabird & Roche, Architectt 





































































































































































































































































































































































































































































































/ J-6 , n-O I /t-o I // O . // O I // O I // O I n-o | ft O \ U O , n-o , n-o . // O //'o * . n'o 



Courtesy, Ilolabird & Roche, Architects 














































































































































































































































































































































































































































































































































































































































Courtesy, Holabird & Roche, Architects 

































































































































































































































































































































294 


STEEL CONSTRUCTION 


FIREPROOFING 

Choice of Concrete. The general subject of fireproofing is dis¬ 
cussed elsewhere in this book. For this building concrete is used for 
fireproofing the steel. It is selected because it protects the steel from 
corrosion, adds to the strength of the columns, and can be placed 
easily, in connection with the concrete used in. the floor construction. 

Thickness Required. The fireproofing affects the steel design 
through the weight of the material 'to be supported, and’through 
the locations of steel members in relation to the openings, as allow¬ 
ance must be made for the thickness of fireproofing. The thick¬ 
nesses required are* 

For exterior columns 4 

For interior columns 3" 

On the bottom and sides of beams 2" 

On the outside of spandrels 4" 

Beyond the edge of shelf angles 
and plates supporting outside 
brickwork 2" 

For the last two items, the brick covering is the fireproofing, but for 
the columns the brick covering is not counted as fireproofing. 

Effect on Position of Exterior Columns, Etc. The requirements 

for thickness of fireproofing control the position of exterior columns, 
spandrel beams, and beams around openings in floors. For example, 
assuming that the steel columns will be 14 inches square, the smallest 
distance that can be used from face of building to center of columns 
is made up of 

One course of brick 4" 

Concrete fireproofing 4" 

One-half of column width 7" 

Total 'lE' 

This value is adopted for the columns along the alley and court 
walls, but along the street fronts a greater distance must be had to 
suit the architectural designs, 1 foot 10 inches being used. The 
columns should be placed as close to the outside of the building as 
possible, to keep the eccentricity small and also to make the pro¬ 
jection of the columns into the rooms as small as practicable. 

In general, the spandrel girders are placed as near the outer 
face of the wall as the fireproofing requirements will permit, that is, 


* To comply with the Chicago Building Ordinance. 




STEEL CONSTRUCTION 


295 


with the edge of the flange 2 inches from the face of the wall. In 
order to provide support farther out, shelf angles or plates are used, 
projecting no nearer to the face of the wall than 2 inches. The 
outer 2 inches of the flange angles of a girder may be considered as 
shelf angles, if the area of this portion of the angles is not required for 
the girder section; and in such a case the girder is placed 2 inches 
nearer the face of the building than otherwise would be done. 

Fireproofing Around Openings. Around openings, the speci¬ 
fications require 2 inches for fireproofing and usually 1 inch is 
needed for plaster, stair facia, or other finish. To these must be 
added the half width of beam to get the distance from finished edge 
of opening to center of beam. The actual amount required varies for 
different sizes of beams. It is usually convenient to use the next 
larger whole number of inches. In most cases 6 inches will suffice 
for the distance from center of beam to finished opening. 

LOADS 

Classification of Loads. The structural frame of the building 
must support the weight of all materials of construction, called the 
“dead loads”; and the loads of all kinds that may be imposed on the 
finished structure, called the “live loads”. Dead loads are, in all 
cases, gravity loads, that is, they act vertically. Live loads are 
gravity loads in most cases. (Belt-driven machinery may cause 
loads in lateral directions.) In addition to the gravity loads, the 
framework must resist wind pressure. 

A design cannot be more accurate than the loads upon which 
it is based. It is, therefore, of first importance that the loads used 
be as accurate as practicable. 

Dead Loads. The so-called dead loads, that is, fixed or immov¬ 
able loads, consist of the weight of all the materials of construction. 
The quantities must be estimated from the architectural plans and 
the structural plans as they develop. 

Unit Weights. The unit weights of some materials will vary 
according to locality and the weights of some will vary because of a 
difference in quality. The following values may be used as aver¬ 
ages for ordinary conditions. Weights which are likely to vary 
with quality, location, or any other cause should be verified or 
corrected by the designer. 


296 


STEEL CONSTRUCTION 


WEIGHTS OF MATERIALS OF CONSTRUCTION 


White pine, spruce, hemlock, per ft., board measure 3 lb. 

Yellow pine, fir, per ft., board measure 4 lb. 

Oaks, maple, per ft., board measure 5 lb. 

Brick masonry, pressed or paving, per cu. ft. 140 lb. 

Brick masonry, hard common, per cu. ft. 120 lb. 

Brick masonry, hollow, per cu. ft. 90 lb. 

Sandstone or limestone rubble, per cu. ft. 140 lb. 

Sandstone or limestone cut facing, per cu. ft. 150 lb. 

Granite, per cu. ft. 160 lb. 

Stone concrete, per cu. ft. 144 lb. 

Cinder concrete, per cu. ft. 96 lb. 

Cinder fill (without sand and cement) per cu. ft. 72 lb. 

Mortar and plaster, per cu. ft. 120 lb. 

Ornamental terra cotta, backed and filled with common 

brick, per cu. ft. 120 lb. 

Marble, per cu. ft. 175 1b. 

Floors, marble, tutti colori, and similar, per sq. ft. 12 lb. 

Windows (glass, frames, and sash), per sq. ft. 5 lb. 

Roofing, composition, per sq. ft. 5 lb. 

Roofing, gravel, per sq. ft. 10 lb. 

Roofing, slate, per sq. ft. 10 lb. 

Roofing, tile,'per sq. ft; 10 lb. 

Roofing, shingle, per sq. ft. 3 lb. 

Sheet metal roofing, cornice, etc, per sq. ft. 3 lb. 

Partition tile, 3 in. thick, per sq. ft. 14 lb. 

Partition tile, 4 in. thick, per sq. ft. 15 lb. 

Partition tile, 6 in. thick, per sq. ft. 22 lb. 

Partition tile, 8 in. thick, per sq. ft. -28 lb. 

Partition tile, 10 in. thick, per sq. ft. 32 lb. 

Floor flat arch (average of set) 8 in. thick, per sq. ft. 28 lb. 

Floor flat arch (average of set) 10 in. thick, per sq. ft. 32 lb. 

Floor flat arch (.average of set) 12 in. thick, per sq. ft. 36 lb. 

Floor flat arch (average of set) 14 in. thick, per sq. ft. 40 lb. 

Floor flat arch (average of set) 16 in. thick, per sq. ft. 46 lb. 

Floor segmental arch tile (average per set) 6 in. thick 

at crown, per sq. ft. 28 lb. 


STEEL CONSTRUCTION 297 

i 

Mortar for tile arch floors, per sq. ft. 3 lb. 

Book tile 2 in. thick, per sq. ft. 12 lb. 

Book tile, 3 in. thick, per sq. ft.. 14 lb. 

Beam tile (when not included w r ith arch tile), per sq. ft. 12 lb. 
Gypsum partition blocks, 3 in. thick, per sq. ft. • 10 lb. 

Gypsum partition blocks, 4 in. thick, per sq. ft. 12 lb. 

Gypsum partition blocks, 5 in. thick, per sq. ft. 14 lb. 

Gypsum partition blocks, 6 in. thick, per sq. ft. 1G lb. 

Plaster on brick, concrete, tile, or gypsum, per sq. ft. 5 lb. 

Plaster on lath, per sq. ft. 7 lb. 

Suspended ceiling complete, per sq. ft. 10 lb. 

Steel bar 1 in. square, 1 ft long, per lineal ft. 3.4 lb. 

Steel plate 1 ft. square, 1 in. thick, per sq. ft. 40.8 lb. 

Cast iron, bar 1 in. square, 1 ft. long, per lineal ft. 3.125 lb. 
Cast iron, per cu. in. .26 lb. 

The following items may vary considerably in weight but the 


values given may be used for preliminary computations, or when 
the quantities are small: 


Iron stair construction, per sq. ft. 50 lb. 

Concrete stair construction, per sq. ft. 150 lb. 

Wood stair construction, per sq. ft. 20 lb. 

Sidewalk lights in concrete, per sq. ft. 30 lb. 

Reinforcment of concrete, per cu. ft. 6 lb. 

Total weight of reinforced concrete, per cu. ft. 150 lb. 

Steel joists, per sq. ft. of floor 6 lb. 

Steel girders, per sq. ft. of floor 4 lb. 

Partition, tile plastered, per sq. ft. 25 lb. 

Same in hotels, per sq. ft. of floor 35 lb. 

Same in office buildings, per sq. ft. of floor 25 lb. 


Live Loads. Live loads are the temporary or movable loads, 
in a building'. They include furniture, merchandise, and people. 
The amount of live load depends on the purpose for which the 
building is used, and for a given purpose may vary greatly from 
time to time and from one part of the building to another. The 
amount to.be used is a matter of judgment, unless an arbitrary 
weight is established by law. In most cities the building ordi- 


298 


STEEL CONSTRUCTION 


nances fix the minimum live loads for various buildings according to 
their use. The requirements of the Revised Building Ordinances of 
the City of Chicago, adopted December 8,1910, are as follows: 


Stores, light manufacturing, stables, and garages 100 lb. 

Office buildings, hotels, and hospitals 50 lb. 

Dwellings, small stables, and private garages 40 lb. 

Churches and halls 100 lb. 

Theaters 100 lb. 

Apartment houses 40 lb. 

Department stores 100 lb. 

Schools 75 lb. 

Roofs 25 lb. 


These loads are to be applied per square foot to the actual floor area 
of the building. 

In designing the floor slabs and joists, the full amount of the live 
load is used. For girders, the live load may be reduced 15 per cent. 
For columns, the load for the top floor is reduced 15 per cent and 
for each successive floor downward the reduction is increased 5 per 
cent till 50 per cent is reached; this final value is used for the remain¬ 
ing floors. This method of reducing the loads on columns is allowed 
in Chicago. Other similar methods are used in other cities. The 
designer must use his judgment as to the propriety of making the 
reductions. 

Special Loads. In addition to the live load, which is assumed 
to be uniformly distributed over the floor, there.may be special, 
loads, such as elevators, machinery, water in tanks, coal in bins, 
space for storage of special materials, etc. The weight of water is 
62.5 pounds per cubic feet, or 8J pounds per gallon; of bituminous 
coal, 50 pounds per cubic feet; of anthracite coal, 60 pounds per 
cubic feet. 

The weights of elevators are usually given by the manufacturer 
for the particular situation. An impact allowance of 100 per cent 
is applied to these weights in designing the beams and their connec¬ 
tions to the columns, but only the actual weights need be allowed 
on the columns. 

Loads on the Building Illustrated. In the Fort Dearborn Hotel 
the following live loads are used: 



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300 


STEEL CONSTRUCTION 


For the roof, per sq. ft. 25 lb. 

For 2nd to 16th floor, per sq. ft. 50 lb. 

For 1st floor, per sq. ft. 100 lb. 

For sidewalks, per sq. ft. 150 lb. 

For freight-receiving room, per sq. ft. 150 lb. 
For stairs, per sq. ft. 100 lb. 


The special loads are the elevator loads as indicated in Figs. 



r height elevator machine. 

Fig. 198. Details of Freight Elevator Machine and Supports 


197 and 198 and water-tank loads shown on the plans of the pent¬ 
house, Plate S. 

The dead loads are computed in connection with the various 
members supporting them, from the unit values previously given. 

































































































STEEL CONSTRUCTION 


301 


The wind load is taken at 20 pounds per square foot of the 
exposed area of the building. 

TYPE OF FLOOR CONSTRUCTION 


Two types of floor construction are suitable for this building; 
the flat tile arch between steel I-beam joists, Fig. 199, and a 



combination tile and reinforced concrete spanning from girder to 
girder, Fig. 200, and Plates J and K. Other types might be consid¬ 
ered but have been rejected as not being suitable for the particular 
requirements of this building. It is evident at once that the type 
using joists requires more steel than the other, but in order to make 
a complete comparison of costs it is necessary to make preliminary 
designs of the steel required for typical panels for each type. 


CONCRETE 





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^TILE 


Fig. 200. Section of Reinforced Concrete and Tile Floor 


Tile Arch Floor. Considering first the flat tile arch, the loads 
per square foot of floor on joists are 


Tile arch set in place 14 in. deep 

43 lb. 

Concrete 3§ in. deep 

42 lb. 

Steel joists 

6 1b. 

Plaster 

5 lb. 

Partitions 

35 lb. 

Total dead load 

131 lb. 

Live load 

50 lb. 

Total load on joists 

181 lb. 











































































8-4 


302 


STEEL CONSTRUCTION 





















































































STEEL CONSTRUCTION 


303 


The loads per square foot of floor, as applied to the girder are 


Total dead load of floor as above 

131 

lb. 

Steel girder 

4 

lb. 

Fireproofing on girder 

2 

lb. 

Total dead load 

137 

lb. 

Live load 85% of 50 lb. 

43 

lb. 

Total load on girders 

180 

lb. 


Therefore, 180 pounds per square feet may be used for both joists 
and girders. 

The allowance for partitions is determined by computing the 
total quantity and weight on one floor and dividing by the number 
of square feet of floor area. 

The depth of the joists is assumed for trial to be 12 inches. 
The joists may be spaced as far apart as 8 feet, but a closer spacing 
is preferred. They may be arranged in the three ways shown in 
Fig. 201. 

The beams 15-22 and 17-24 support the wall load as well as the 
floor load. The amount of the wall load is calculated as follows: 


Gross wall area ll'-0"Xl9'-4" 
Less windows 2x6'-4"x4'-0" 

Net wall area 


212 sq. ft. 
51 sq. ft. 

161 sq. ft.. 


Weight of material composing wall is 

4 -inch pressed brick weighing 140 lb., per cu. ft. 47 lb. 

4-inch common brick weighing 120 lb., per cu. ft. 40 lb. 

4^-inch hollow brick weighing 90 lb., per cu. ft. 34 lb. 

Total weight per sq. ft. of wall area 121 lb. 

Using even figures, the weight of wall on the spandrel beam is 

160X120 = 19,200# 

Scheme a. In scheme a, Fig. 201, the sizes of beams required 
to support the loads computed above are as marked on the diagram. 
The lengths used in computing are the actual lengths of the beams, 
that is, allowance is made for the width of column. Thus the joist 
between columns 16 and 23 is taken at 18'-2" long, and because it is 
shorter than the other joists it is made lighter. 

Scheme h. Scheme b, Fig. 201, is similar to scheme a, the only 
difference being in the spacing and, consequently, in the weight of 
the joists. It has the advantage of using joists all alike and equally 





304 


STEEL CONSTRUCTION 


spaced. It hasthe disadvantages of greater weight (slight), greater 
number of pieces to be handled, and of not providing a direct brace 
between columns 16-23. ( 

Scheme c. In scheme c, Fig. 201, the direction of the joists 
differs from that in the other schemes. It has the disadvantages of 
a greater variety of sizes of joists and of throwing a heavy load on 
the spandrel girders which have eccentric connections to the columns. 
Its advantage (which is not apparent from the sketches but is shown 
on the architectural plans of the building) is that the girders do not 
cross the corridor which extends along the middle of the building 
alongside of columns 16-23. 

The weights of the steel in the three schemes differ so little that 
this feature would not govern. Scheme a seems to be the best one 
because it has the least number of pieces to handle, braces all col¬ 
umns iu both directions, and loads the columns with the least eccen¬ 
tricity. 

Problems 

1. Estimate the weights of steel in the panels shown in Fig. 201 for schemes 
a, 6, and c. 

2. Check the sizes of I-beams used in schemes a, b, and c. 

Combination Tile and Concrete Floor. Now consider the 
type of floor construction shown in Fig. 200, that is, the combina¬ 
tion tile and concrete. There being no steel joists, the weight per 
square foot as applied to the girders is estimated as follows: 


Concrete slab 3| in. 

42 

lb. 

Concrete joists 4"X10", 40# X| 

30 

lb. 

Tile 10"X12";32#X1 

24 

lb. 

Plaster 

5 

lb. 

Reinforcing steel 

3 

lb. 

Girder steel 

4 

lb. 

Girder fireproofing 

10 

lb. 

Partitions 

35 

lb. 

Total dead load \ 

153 

lb. 

Live load, 85% of 50 lb.^ 

1 43 

lb. 

Total load 

196 

lb. 


On the narrow panels the tile fillers are 8 inches deep, the resulting 
saving in weight of tile and concrete and concrete joists being 9 
pounds. This leaves a total weight of 187 pounds per square foot 
on these narrow panels* 


STEEL CONSTRUCTION 


305 

Two schemes for the arrangement of girders are shown in Fig. 
202. In both cases the spandrel beams have the same wall load as 
computed in connection with the tile arch type of floor, viz, 19,200 
pounds. The sizes of beams required are marked on the diagrams. 
Note that in scheme a the lighter load applies in the narrow panel, 
whereas in scheme b the heavier load must be used in both panels. 




Fig. 202. Diagram Showing Framing for Combination Tile and Concrete Floor 


The members marked S are struts which support only narrow 
strips of floor load but are required to brace the columns in the 
direction in which girders do not occur. For this purpose light 
I-beams or H-sections are commonly used, but in this case reinforced 
concrete is used. 

Neither scheme has any definite advantage in weight of steel. 
Scheme a is adopted because the arrangement is better suited to the 
plan of the floor. The girder 16-23 is alongside the corridor and is 
covered by the partition. No girder crosses the corridor. The use 
of the larger spandrel beams assists in bracing the building. A 

























306 


STEEL CONSTRUCTION 


definite disadvantage is that the spandrel beams, carrying large 
loads, have eccentric connections to the columns. 

Problem 

Check the sizes of beams given in Fig. 202. 

Selection of Floor Type. The selection of the type of floor con¬ 
struction is affected by a number of items in addition to the cost of 
the steel, which cannot be considered in detail here. Some of them 
are: the effect of difference in weight on the cost of the columns; 
the effect of the difference in weight on the cost of foundations; the 
relative cost of the floors; the thickness of the floor construction; 
and soundproof ness. In this particular case the cost of the steel 
is the most important item. 

The combination type is used for this building on account of 
its economy, all conditions being considered. Plates J and K. 

FRAMING SPECIFICATIONS 

Arrangement of Girders. Some attention has already been 
given to the arrangement of the girders in the discussion of 
typical floor panels, but this arrangement really needs to be con¬ 
sidered in its relation to the entire building. Refer to the archi¬ 
tectural and the framing plans of the typical floors, Plates R and G. 

Exterior. It is necessary of course to have girders around the 
entire perimeter of the building to support the walls. 

Interior. The next thing to settle is whether the interior 
girders shall be parallel to or perpendicular to the outside lines of 
the building The former arrangement is used. It is to be noted 
that the girders and their covering project several inches below the 
ceiling line, hence it is important to place them so that they interfere 
as little as practicable with the interior arrangement. In the plan 
adopted the principal lines of girders are along the side of the corri¬ 
dors and thus can be partially or wholly concealed. They cross the 
corridors only at two places. 

The arrangement used gives practically a set of duplicate floor 
panels along the outside walls of the building and another along the 
court walls. The other plan would be nearly as good in this respect. 
However, columns 2 and 6 are not opposite the columns in the next 
row so that if girders perpendicular to the outside lines were used, 
they would be connected at one end to the columns mentioned but 


STEEL CONSTRUCTION 


307 


would require cross girders to support the other ends. Having main 
lines of girders east and west, and also north and south, is advanta¬ 
geous in bracing the building. 

Special Cases. On the first floor, Plate C, girders are required 
between columns 17-19 on account of the length of span. Along 
the east and south sides no wall girders are required because the 
basement walls can be used to support the first-story walls, hence 
along these two sides the girders are placed perpendicular to the 
side lines. Other interior girders are placed so as to give the greatest 
possible uniformity in the floor construction. 

Around openings, such framing is used as may be needed. No 
instruction is necessary for this, as the framing required can easily 
be determined from the conditions in each case. 

Each building has its special conditions affecting the placing 
of the girders. Flat ceilings, permitting no projecting beams, may 
compel the placing of girders on the short spans and perhaps the 
use of double girders. The use of reinforced concrete floors with 
rods in two directions requires girders on all four sides of the panels. 
Pipe shafts in line with the columns in one direction may require 
the placing of the girders in the other direction. .Columns in rows 
in one direction, only, limit the girders to those lines. 

Arrangement of Joists. Having established girder lines, the 
joists, if used, are spaced as uniformly as practicable. A joist should 
connect to each column in order to brace it, and the intervening 
panels should be divided into a number of equal spaces. Their 
spacing is governed in most cases by the type of floor construction; 
for the style of construction adopted no steel joists are required. 

Beam Elevations. The elevations of beams are given in refer¬ 
ence to the elevations of the floors. The distance from the floor 
lines to the top of the beams is governed by the floor construction. 
The items entering into this dimension are: the thickness of flooring, 
whether of wood, marble, tutti colori, etc.; the mortar bed for 
setting marble and similar floors; the thickness of the w r ood nailing 
strips for wood floors; the space for electrical and other conduits. 

The minimum thickness of concrete floors over beams should 
be 3 inches to allow space for conduits and to prevent cracks. Other 
floors require from 3 to G inches, depending upon conditions. 

In flat tile arch construction the total thickness "is fixed by the 


308 


STEEL CONSTRUCTION 


depth of the typical joist. All beams deeper than this will be placed 
flush on top, and all beams shallower flush on the bottom. Thus, 
if the typical joist is 12 inches, the girder, which probably is deeper, 
will be placed flush with the top of the joist and will project below 
the ceiling line; other joists and framing around openings which 
may be 8-, 9-, or 10-inch beams will be placed flush^with bottom 
to provide bearing for the skew back of the arch at the proper level. 

For combination tile and concrete, and for concrete floors, all 
the beams will be placed flush on top except such as may require a 
different elevation to suit some special condition. 

Spandrel beams, being embedded in the walls, are not governed 
by the elevation of the floor. In many cases these beams serve as 
the lintels over the windows and their elevations are fixed accord¬ 
ingly. This is shown in the spandrel sections, Plates L and T. 

For flat roofs, the beams may be set on slopes parallel to the 
roof surface, or may be set level, depending on whether the roof or 
the ceiling has the greater control. 

Arrangement of Columns. Location. It is desirable that the 
columns be arranged in rows across the building in both direc¬ 
tions, but this may be prevented by the arrangement of the rooms 
in the building. The column spacing is also affected by the design 
of the exterior; the layout determined by the architectural require¬ 
ments governs in most cases. Thus in the problem the position 
of column 18 is fixed by the light court wall; of columns 19 and 26 
by the space required for elevators and stairs, Plate R; of column 
33 in the lower part of the building, to suit the arrangement of rooms 
in the first story, Plate N, it being offset at the fourth floor, Plates Q 
and R, on account of the light court wall. The spacing of the col¬ 
umns along the west fagade conforms to the architectural treatment, 
an odd number of panels being used to allow an entrance at the 
center. The spacing along the north fagade is governed chiefly by 
the interior divisions. 

Distance from Building Line. The distances of the columns 
from the building lines are governed by the fireproofing, as has been 
explained. They are l'-lO" along the north and west fagades, l'-3" 
along the alley and court, and l'-0" along the south side. This 
latter value is used because provision is made for a building on the 
adjoining lot which will supply any additional protection needed. 


STEEL CONSTRUCTION 


309 


DESIGN OF STEEL MEMBERS 

Design of Beams. The spacing of columns, arrangement of 
girders, and type of construction being settled, the next step is the 
design of the beams. 

Joists. There are no joists except in a few cases and these can 
better be classed as special beams. Joists when used are almost 
invariably simple beams with uniformly distributed loads. There¬ 
fore, having computed the total load per square foot of floor, and 
having fixed the span and spacing, the total load on the beam is the 
product of these three quantities, and from it the size of beam is 
taken from the tables. Or, if the size has been selected, the capac¬ 
ity for the given span can be taken from the tables; and from this 
the floor area which it will support, and then the maximum spacing 
can be determined. The length of span and of load area used is the 
distance, center to center, of girders if the joist frames between 
girders, and the actual length of the joist if it connects to columns. 

Girders. The typical girders were designed in connection with 
the preliminary study of the floor construction. The special cases 
remain to be designed. For example take girders 8-9 and 10-11. 

Girder 8-9 typical floor, Plate F, span 18'-6". Load area on 
one side only. 

Total load u. d. 18'-6"X10'-0"X196# = 36,260# 

This requires a 15" I 42 # 

Girder 10-11 typical floor, span 15'-3". Heavier slab north side, 
lighter span south side. 

/15'-3" X10'-O" X196 # = 29,890 # 

Total load u. d. ^ 15 /_ 3 * x ^-(fX 187# = 17,110# 

47,000# 

This requires an 18" I 46#* 

On the first floor all the slabs are built with 10-inch tile and 
provision is made for a marble or a tutti colori floor. The live load 
allowance is 1Q0 pounds per square foot. The partition allowance 
can be reduced to 20 pounds per square foot because of the 
larger rooms. Therefore, the load per square foot carried by the 
girder is 


♦ Light weight Carnegie beam. These special beams are not always available. 




310 


STEEL CONSTRUCTION 


Marble floor 10 lb. 

Mortar 10 lb. 

Concrete slab 3^" . 42 lb. 

Concrete joists 4" X10", 40 # XI 30 lb. 

Tile 10"X12", 32#Xf 241b. 

Plaster 5 lb. 

Reinforcing steel 3 lb. 

Girder steel 4 lb. 

Girder fireproofing 10 lb. 

Partitions 20 lb. 

Total dead load 158 lb. 

Live load 85% of 100 lb. 85 lb. 

Total load 243 lb. 


Applying this to girder 8-9, which has a span 18'-6", gives 

Total load u. d. 18'-6"X19'-5"X243# = 87,480# 

This requires a 24" I 69§ # 

Problems 

1. Design girder 9 - 10 , typical floor; girder 17 - 19 , first floor; and girder 
13 - 20 , first floor, Plates F and C. 

2. Compute the total load per square feet of floor in the freight room on 
the first floor (panel 29 - 30 - 87 - 36 ). Floor, a reinforced concrete slab 8 inches 
thick. See Plates C and N for construction of floor. No partitions. Live 
load 150 pounds. Design the beam across the center of the panel. 

3. Compute the load on the roof girders, and design girders 8 - 9 , 9 - 10 , 
and 10 - 11 . (See Plates G and J.) 

Spandrel Girders. The spandrel girders in this design carry in 
most cases one-half panel of floor load and a panel of wall. The 
spandrel girders of the typical * panels of the typical floors were 
designed in the study of the floor types. 

The spandrel girder 1-8, typical floor, carries only the wall 
load; this is practically uniformly distributed. The wall in this 
panel is 17 inches thick; its weight per square foot of surface is 
computed thus: 

4 in. pressed brick, 140 lb., per cu. ft. 47 lb. 

8^ in. common brick, 120 lb., per cu. ft. 85 lb. 

4§ in. hollow brick, 90 lb., per cu. ft. _34 lb. 

166 lb. 

The wall surface is the panel area less the window area, viz, 
ll'-0"Xl8'-4" 201 sq.ft. 

Less 2x3'-6"X6'-0" 42 sq. ft. 

Net area 159 sq. ft. 


STEEL CONSTRUCTION 


311 


Therefore the weight on the girder is 

166X159 = 26,400# 

The span is 18'-6". This requires a 15" I 36#. More exact compu¬ 
tations would take into account the position of the windows, weight 
of concrete around beams, and weight of girder, but would not 
change the result in this case. 

The effect of the wind stresses on the spandrel girders is con¬ 
sidered later in the text. 

Problems 

1. Design spandrel girder 1 - 2 , typical floor. 

2. Design spandrel girder 10 - 17 , typical floor. 

3. Design spandrel girder 18 - 17 , typical floor. 

Special Beams. Special beams are required around elevators 
and stairs, and for the support of elevator machinery, chimney, 
penthouses, and tanks. 

Panel 30-31-38-37. The panel 30-31-38-37 contains several 
special features, viz, a stairway, an elevator shaft, a chimney and 
vent space, and a pipe shaft. There is only a small section of floor 
in the panel, adjacent to column 37 on the typical floor. 

In the north half of the panel the 8-inch I-beams support only 
partitions. None of them are fully loaded, but this size is considered 
the minimum for this situation. 

The stair load may be taken at 50 pounds per square foot for 
the dead load and 100 pounds per square foot for the live load. 
It is supported by the 8-inch I-beam near column 37, and the span¬ 
drel beam 31-38. The latter beam cannot be placed at the floor 
level because the windows just above the stair landing interfere, so 
it must be placed near the level of the stair landing. 

Framing around stairwells should be so designed that the weight 
of the stair can be supported from either the sides or the ends. In some 
cases the entire stair load is carried by the stringers to the beams at 
the ends of the well and in other cases hangers and struts transmit 
the loads to the side beams. Usually this cannot be determined 
by the structural steel designer unless he designs the stair. 
Problem 

Design the cross beam near the middle of panel 30 - 81 - 38 - 87 , typical floor. 

Panel 19-20-27-26. The special framing in the panel 19-20- 
27-26 , Fig. 197 and Plate F, provides for elevators and stair. It 
presents no unusual features. 


312 


STEEL CONSTRUCTION 


10th Sty. 

5,200 
29,000 
e 12,400 

e 8,500 

7,600 

62,700 

501,900 

30,000 

| 531,900 

inlao 

n\*r V r?i«c 

X-r X 

s-* 02 r“ 

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11th Sty. 

O o O O Q 

O O O O O 

aT cm ao* i>" 

CM H 

0> QJ 

63,200 

439,200 

30,000 

469,200 

12th Sty. 

6,200 
29,000 
e 12,400 
e 8,500 
7,600 

63,700 

376,000 

30,000 

| 406,000 

•rtl* X 

GJ x 

_ «o 
~ tn 

i— 1 Tf 

13th Sty. 

6,700 
29,000 
e 12,400 
e 8,500 
7,600 

64,200 

312,300 

30,000 

| 342,300 

14th Sty. 

38388 

»—<1 O lO CC 

^ToTncxT t>" 

CM 1-H 

0> 0) 

2 

oo" 

5 

30,000 

| 278,100 

«|oo V 

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jr* tn 

Ch_| 

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' 15th Sty. 

O Q O Q Q 
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i>" cT cm" go" u- 

CM 

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o 

io" 

;o 

183,500 

30,000 

213,500 

>> 

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118,400| 

30,000 

148,400 

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rT 03 

Q,_j 

Attic 

4,800 
17,100 
e 16,000 
e 6,300 
7,600 

8 

30 

s 

X 

lO 

30,000 

81,800 

Pent 

House 

• • • • • 

• • • • • 

• • • • • 

• • • • • 







Floor Live Load . 

Floor Dead Load . 

Wall Load, 8-1 . 

Wall Load, 8-15 . 

Column and Covering; . 

Total for Story . 

Accumulated Total . 1 

1 Eccentric Effect . 

I Total . 

Column Section . 


a 

d 

a 1 

05 

o 

05 

^H 

05 

S 


u 

o 


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"O 

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Of 


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£ 


Sub 

B’sm’t 







Basement 

88 : :8 
iOO • • CO 

o" o" : :oo" 

CO 

0) <D . • 

47,800 

1,129,200 

c© 

1,175,700 

nN 1 

«|H» X »ft|ao 

Xrt-X 

GJ X2 
' © ' 
E_j£ 

© 

1st Sty. 

88888 

GO CO 00 

Tf Cl N £ c 

CO r-H *-H r— < 

Q 0) 

76,100 

1,081,400 

6,900 

1,088,300 

2nd Sty. 

4,800 

29,000 

e 14,600 

e 8,500 

9,300 

66,2001 

1,005,3001 

30,000 

1 ,035,300 

x h|h«|v 

X'T XX 
m x^r '=>■ 

S jSE 

3rd Sty. j 

4,800 

29,000 

e 13,500 

e 8,500 

7,600 

63,400 

939,100 

30,000 

001‘696 

4 th Sty. 

4,800 
29,000 
e 12,400 
e 8,500 
7,600 

62,3001 

875,700 

30,000 

905,700 

"I* to 

«h*X *"■ 

X x 

5th Sty. ^ 

4,800 
29,000 
e 12,400 
e 8,500 
7,600 

62,300 

813,400 

30,000 

CC 

00 

1 PI. 1 

4Ls 6 

4 PI. 1 

| 6th Sty. 

O O O Q O 
o o o © o 
oo^o^io o 

tF cT in oo t2' 

CM —I 

4J 0> 

62,300 

751,100 

30,000 

781,1001 

«N« 

«IH« \S n\-+ 

x£x 

■m y-r 

XX 1 

. 

S _J Oh 
^ CM 

7th Sty. 

4,800 
29,000 
e 12,400 
e 8,500 
7,600 

62,300 

688,8001 

1000‘0£ 

718,800 

8th Sty. 

4,800 
29,000 
e 12,400 
e 8,500 
7,6001 

62,300 

626,500 

30,0001 

i© 

scT 

8 

«|H* N/ H|N 

x-f X 
GiX^; 

oq 

0h_| Oh 

-h ^ CM 

9th Sty. 

88888 
oo cq 

TtTcTcMOOl^" 

CM H 

O 0> 

62,300 

564,200 

30,000| 

594,200 


Floor Live Load. 

Floor Dead Load . 

Wall Load, 8-1 . 

Wall Load, 8-15 . 

Column and Covering 

1 Total for Story. 

| Accumulated Total. . . 

| Eccentric Effect . 

1 Total . | 

Column Section . 


Fig. 203 (Continued) 





















































































STEEL CONSTRUCTION 


313 


Penthouse. The penthouse, Plates G and S, between columns 
29-31-38-36 contains a number of special items. Beams are re¬ 
quired at the roof level to support the penthouse walls. At the roof 
level near columns 29-36, two 18-inch I-beams are provided for the 
purpose of carrying two water tanks and the concrete platform on 
which they rest. 

The machine platform, Plate S, at an elevation of about 18 feet 
above the attic floor, supports the freight elevator and its machinery. 
The arrangement of the sheave beams and the machinery, and the 
loads are given in Fig. 198. As previously directed, these loads 
must be doubled for the beams and their connections. It is not 
worth while to figure closely on the elevator supports. Only a 
small amount of material is involved, so all the computations should 
be on the safe side. 

With the liberal treatment of the elevator loads suggested 
above there remains nothing complicated in the designing of the. 
penthouse framings, but the work is tedious on account of the 
variety of loads and the irregular spacings. 

Problem 

Check the framing in the penthouse between columns 29-31-38-36, Plates 
G and S. 

Sidewalk Construction. The sidewalk framing is shown on the 
first floor plan of the building, Plate C. A strip of prismatic lights 
extends along the building line, Plate K. 

Problem 

Check the sizes of beams used in the sidewalk. 

Design of Columns. Columns 8 and 9 are selected as typical 
exterior and interior columns for illustrating the computation of 
loads and the design. 

Loads on Column 8. Fig. 203 gives the schedule of loads on 
column 8. The floor area tributary to the column is 19'-5"X9'-10", 
or 191 square feet; for convenience use 190 square feet. This area 


applies at all floors and the roof. 

The dead loads are 

Roof, per sq. ft. 90 lb. 

3rd to attic floors, per sq. ft. 153 lb. 
2nd floor, per sq. ft. 170 lb. 

1st floor, per sq. ft. 158 lb. 


314 


STEEL CONSTRUCTION 


The live loads per square foot for the successive floors after 
making the reductions described on p. 298 are, 


Roof 

25 lb. 

9th floor 

25 lb. 

Attic floor 

42± lb. 

8th floor 

25 lb. 

16th floor 

40 lb. 

7th floor 

25 lb. 

15th floor 

37* lb. 

6th floor 

25 lb. 

14th floor 

35 lb. 

5th floor 

25 lb. 

13th floor 

32* lb. 

4th floor 

25 lb. 

12th floor 

% 

.£ 

O 

CO 

3rd floor 

25 lb. 

11th floor 

27* lb. 

2nd floor 

25 lb. 

10th floor 

25 lb. 

1st floor 

50 lb. 


Column 8 supports one-half of the wall between columns / 
and 8, and one-half between columns 8 and 15. As these panels 
of wall are not the same thickness, they are estimated separately. 
Their respective weights have been estimated to be 166 pounds and 
121 pounds per square foot for wall surface. 

The wall area estimated is the net area between columns, the 
width of column for this purpose being taken at 22 inches, out to 
out, of concrete. The brick facing for this width is estimated 
with the weight of the column. Between columns 1 and 8 in the 
typical story, the total wall area is ll'Xl7'-8" or 194 square feet. 
From this is deducted the window area, Plate V, 2 X 3'-6" X 6'-4" 
or 44 square feet, leaving a net area of 150 square feet. One-half 
of this, 75 square feet, is carried by column 8. At other stories 
the area differs because of different story heights and different 
windows. At the roof in this panel are a terra cotta balustrade 
and a cornice, Plate T, and at the 3rd and 4th floors are belt courses 
of terra cotta projecting beyond the wall line. These are irregular 
in shape but their dimensions can be scaled and their approximate 
weights computed at the rate of 120 pounds per cubic foot. 

Between columns 8 and 15 in the typical story, the area sup¬ 
ported by column 8 is ll'Xl7'-6" or 192 square feet. From this is 
deducted the window area 2x4'x6'-4" or 51 square feet, leaving 
a net area of 141 square feet. One-half of this, 70 square feet, is 
carried by column 8. Note that the small window is neglected. 

At the roof there is a parapet wall the dimensions of which can 
be scaled from the drawings. 


STEEL CONSTRUCTION 


315 


The basement and first story walls are not supported by the 
steel framework. 

For the weight of the column and covering an average amount 
per foot o? length is computed and used for the whole length thus: 

Steel 150 lb, 

Concrete (22x22 less 40) say 450 lb. 

Brick facing 4" X 22" say 901b. 

690 lb. 

This amount is too large at the top and too small at the bottom. 

From the foregoing data the loads on column 8 are computed 
and entered in the schedule in Fig. 203. For the column section in 
any given story the loads entered are the weight of the column in 
that story, the w r eight of the floor above, and the weight of the walls 
in the story above. 

As the loads are entered, the eccentricity, if any, is noted as 
indicated by the letter e. At all floors from the second to the 
roof, one-half of the floor load comes to the column through the 
girder 8-9 and one-half through 8-15. These connect on opposite 
sides and balance each other. At the first floor the entire floor 
load connects to one flange and, therefore, is eccentric. The wall 
loads are eccentric throughout, but at the second floor the wall load 
1-8 is only slightly so and is on the opposite side of the axis from 
the wall load 8-15. In the schedule, on the line marked “eccentric 
effect”, are given the concentric equivalents of the eccentric loads 
computed from the formula 

r 

No serious error is committed if, for the shape of column here used, 
the value of r is taken at eight-tenths of c. The result can be checked 
back and the error corrected, if necessary, after the section has been 
selected. The values in the schedule are computed on this basis 
but the amount entered is three-fourths of the computed amount. 
Thus for the attic story column the computations are 

W',= 22,300X^r =40,600, say 40,000# 
oXo 

Three-fourths of this is 30,000, which amount is used. At all the 
typical floors, the result is so close to this amount that it may be 
used from the second story to the roof. 



316 


STEEL CONSTRUCTION 


10th Sty. 

8,800 

48,000 

5,600 

62,400 

| 496,000 

1 000 6 

505,000 

.ftlao 

V «l« 

X^X 

V" ■'T 

11th Sty. 

9,600 

48,000 

5.fi00 

63,2001 

433,600| 

1000 6 

442,600 

S _j s 

tN 

12th Sty. 

10,400 

48,000 

5.600 

64,0001 

370,400 

000 6 

379,400 

iftlao 

"" N X 

X-£ 

<M V 

| 13th Sty. 

11,200 

48,000 

5,600 

64,8001 

306,400 

000 6 

1 315,4001 

** CO 

SJ 

1—1 

' 14th Sty. 

12,000 

48,000 

5,600 

65,600 

1 241,600 

000 6 

250,600 

HS 

?*X 

x^ 

M X 

' 15th Sty. 

12,800 

48,000 

5,600 

66,400 

176,000 

000 6 

185,000 

CO 

SJ 

16th Sty. | 

13,600 

48,000 

5,600 

67,200 

109,600 

000 6 

51,4001 118,6001 

«|a0 

n|ao 

Xco 

2 X 

r-H Tf 

Attic 

8,000 

28,800 

5,600 

42,400 

42,400 

9,000 

Pent 

House 








Floor Live Load. 

Floor Dead Load. 

Column and Covering. 

| Total for Story. 

| Accumulated Total. 

1 Eccentric Effect. 

| Total. 

Column Section. 


O 

N 

co 

r3 

o 


O 

O 


'D 

a 

o 

-5 


d 

Q 

o 

03 


3 

£ 



Fig. 204 (Continued) 

















































































STEEL CONSTRUCTION 


317 


The eccentric effect at the first floor (on basement column) is 
U", = 39,500 X = 62,000 # (approx.) 

0X0 

three-fourths of this is 46,500 pounds. 

Note that the eccentric effect is not cumulative. 

Loads on Column 9, The loads on column 9 are much simpler, 
consisting only of the weight of the column and the floor loads. The- 
floor area is f9'-5" X 16'-6" or 320 square feet. On the floors, second to 
attic, the part of this area in the panel 9-10-17-16 is lighter than the 
rest of it. This is taken into account in the following dead loads: 


Roof, per sq. ft. 90 lb. 

3rd to attic, floors, per sq. ft. 150 lb. 

2nd floor, per sq. ft. 167 lb. 

1st floor, per sq. ft. 158 lb. 

The weight of the column per lineal foot is 

Steel 150 lb. 

Concrete (20X20 less-40) 360 lb. 

Total 510 lb. 


At each floor there is eccentricity due to the unequal loads from the 
girders 8-9 and 9-10. On all floors from second to roof 160 square 
feet of the total area are applied to the column through girder 9-16 
which connects to the web and is not eccentric; 96 square feet are 
applied through girder 8-9 ; and 64 square feet through girder 9-10. 
The difference between the last two amounts, 32 square feet, is the 
unbalanced area producing eccentricity. 

The loads in the schedule for column 9, Fig. 204, are computed 
from the foregoing data. 

The eccentric effect is small and to save tedious calculations 
can be computed for average conditions at a typical floor and the 
result applied to all floors except the first. Thus, at the fourteenth 
floor the total of dead and live loads is 60,000 pounds; one-tenth of 
this, or ,6,000 pounds, is unbalanced and, hence, is eccentric. The 
values of 6 and c are eciunl and may be assumed / inches, t may be 
assumed 5 inches. 

W' e = 6,00 r QX / — = 12,000# (approx.) 

5x5 

According to the rule adopted three-fourths of this amount is used, 
that is, 9,000 pounds. , This is applied at all floors except the first, 





318 


STEEL CONSTRUCTION 


where the load conditions are different. After the column section 
is selected, the eccentric effect may be checked, using the actual 
values of e, c, and r. 

Column Section. Type. The column section adopted for this 
building is the H-section built of plates and angles. It is selected 
because of its ease of manufacture, ease of making connections both 
to web and to flanges, and for commercial reasons. 

Location. The position of the column as to the direction of 
greatest stiffness has been discussed, and in both of the examples 
the column is placed so that the stronger way resists the eccentric 
moment of the load. 

Size. It is desirable, though not of great importance, that the 
general size of the column be maintained throughout the height. 
For this reason a 12-inch web plate is used, although this might be 
made 10 inches in the upper stories and 14 inches in the lower stories. 
If column 8 were made 10 inches in the upper stories, the eccentric 
effect would be so increased that the section required would prob¬ 
ably be greater than for the 12-inch column. The use of the 14-inch 
web plate in the lower stories would decrease the weight of the 
columns but would make the finished columns larger and thus reduce 
valuable floor space? 

Length. The columns are made in two-story lengths, the 
splices in this case being made at the even numbered floors, that is, 
at 2, 4, 6, etc. The columns which extend through the sub-basement 
are made in three-story lengths to bring the splice at the second 
floor so as to be at the same level as the others. The cross section 
of any length of column is governed by the stress in the lower of 
the two stories comprising that length. 

Summary. Having the loads computed as given in the sched¬ 
ules and having established the foregoing general conditions, it only 

remains to select from the tables in the handbooks the sections 

< 

required for the several lengths of column and enter them in the 
schedule. (See also Plate H). 

In designing these columns* the maximum thickness of metal 
used is | inch, because any metal thicker than this would require 
reaming or drilling and thus add to the cost. When the total thick- 

*The tables referred to on pp. 189 and 194 were not used in making this design; so tne 
identical section uiay not be found therein. 



STEEL CONSTRUCTION 


319 


ness of cover plates on one flange is more than \ inch, two or more 
plates are used, each being | inch or less in thickness. No cover 
plates are used unless the stress is beyond the capacity of a section 
having f-inch metal in the web plate and angles. 

Problems 

1. Compute the loads and make the design for column 16. (Note that 
this column extends through the sub-basement.) Make schedule as in Figs. 
203 and 204. 

2. Compute the loads and make the design for column 17 (Note that 
the court walls do not occur below the third floor.) 

3. Make a diagram showing the floor areas supported by column 17 at 
the first, second, third, and typical floors, Plates C, D, E, and F. 

4. Give detailed computations of the wall load supported by column 17 
in a typical story, Plates F, R, and W. 

Column Pedestals. The piers under the columns are round and, 
therefore, in order to distribute the load as evenly as possible, round 
cast-iron pedestals of the type shown in Fig. 152 and Plate H are 
used. The bearing allowed on the masonry in this case is 800 
pounds per square inch. The load for column 8 is 1,129,000 pounds 
and for column 9 is 1,132,000 pounds. (The eccentric effect is not 
included.) The area required is 1415 square inches, which corre¬ 
sponds to a circle 42 inches in diameter. But for the sake of using 
few patterns, the diameter is made 44 inches. 

Height. While the height of the pedestal is taken at 24 inches, 
there is no very definite way of determining the height. However, a 
number of trial designs indicate that pedestals of the type here used 
should be proportioned as follows: 

For a bearing of 800 lb. per sq. in., height 53% of diameter 

For a bearing of 600 lb. per sq. in., height 43% of diameter 

For a bearing of 400 lb. per sq. in., height 35% of diameter 

Top. The size of the top of the pedestal is controlled by the 

detail of the base of .the column. It must extend far enough beyond 
the hub to provide holes for connecting to the column; 2\ inches at 
the narrow place is usually enough and this is available to resist the 
bending moment. The thickness is assumed arbitrarily at \ \ inches. 

Ribs. The number of ribs assumed is eight. Their thickness 
is not less than one-twentieth the height, that is, inches. 

Diameter of Hub. The diameter of the hub is made such that 
the greater part of the column section is directly over it. In this 
case 11 inches inside diameter is suitable. The thickness of the hub 


320 


STEEL CONSTRUCTION 


I 


must be such that its area together with that of the ribs under the top 
plate will support the column load at 10,000 pounds per square inch. 
Thus the total area required is 113 square inches. The area of the 
ribs to be counted is 8X2£"X1£" or 25 square inches, thus leaving 
88 square inches to be provided in the hub. This requires 2j inches 
thickness of metal, which makes the outside diameter 15§ inches. 
The area of the 11-inch circle is 95'square inches, and of the 15^-inch 
circle 188 square inches; the difference, 93 square inches, is slightly 
more than required. 

The thickness of the bottom plate must be assumed for trial; 
use 2f inches. 

The dimensions of the rim are fixed arbitrarily \\ inches thick 
and 5 inches high. 

Test for Resistance to Bending. Having determined or assumed 
the thickness of metal in the various parts of the pedestal, it is now 
necessary to test the cross section for its resistance to bending. 
The procedure is the same as that given on p. 220. 

Center of Grainty. To locate the center of gravity and the 
neutral axis, take the following: 

Bottom plate area 41X21 =112.75 M112.75X 1.375= 155.05 

Hub area 2X191X21= 88.90 M 88.90X12.625 = 1122.36 

Top plate area 2X HX21= 7.50 M 7.50X23.25 = 174.37 

Rim area 2X 5 Xlj= 15.00 M 15 X 5.25 = 78.75 

224.15 1530.53 


The distance of the neutral axis from the bottom 


1530.53 

224.15 


or 6.85 inches. 


of the plate is 


Moment of Inertia. The moment of inertia of the section about 
the neutral axis is 


For bottom plate 

i = 

For hub 

1 = 

For top plate 

1 = 

For rim 

1 = 


fyj X41 x(2.75) 3 = 71 

\l 12.75 X (5.48) 2 = 3386 

(ts X2.25X(19*75) 3 X2 = 2880 

\88.9X (5.78) 2 = 2969 

f T SjX2.50X(1.5) 3 X2 = 1 

\7.5 X(16.4) 2 = 2018 

(ts Xl|X(5) 3 X2 = 31 

\l5.0X (1.6) 2 = 38 


Total moment of inertia = 11,394 






STEEL CONSTRUCTION 


321 


Resisting Moment. The resisting moment of the section is 

t i i f 3000X11,394 . nnn nnn • n 

R M =-——-=4,990,000 m.-lb. 

6.85 

The bending moment of the load is 

M = 1,132,000X44 = 4,980,000 in .-lb. 

Hence the assumed plate has the required resistance to bending. 


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Fig. 205. Diagram Showing Bending Moments Due to Wind Pressure 


At columns 36, 37,38, 40, 4U and 42 , the piers are built centrally 
on the lot line to support two sets of columns. The bases cannot be 
extended beyond the lot line, so are made rectangular. Three 




























I 


322 STEEL CONSTRUCTION 

I-beams are used for this purpose, as illustrated in Plate H. The 
method of designing has been explained under bearings for beams. 


WIND BRACING 


Wind Loads for Entire Building. The wind load is assumed 
to be 20 pounds per square foot, all of which is to be resisted by the 
steel frame. Fig. 205 is a diagram on which are marked the wind 
loads for the successive stories and the resulting bending moments 
in the columns and the girders. The values given are for the entire 
building and, as the building happens.to be practically square in 
plan, the diagram applies for both directions. 

At each of the upper floor levels, the load applied to the frame¬ 
work is 100X11X20 or 22,000 pounds. The first, second, and third 
floors support different areas, hence different loads. 

Bending Moments. In Columns. The bending moments in 
the columns are computed as follows: 


Attic 

22,000 x 5* = 

16th story 

44,000X5* = 

15th story 

66,000X5* = 

etc., etc. 


1st story 

382,500x7* = 

Basement 

397,000X6 = 


121,000 ft.-lb. 


In Girders. The bending moments in the girders, according 
to the rule previously established, are the means between the bending 
moments in the columns. The values are 


Roof 

Attic floor 

10th floor 
etc., etc. 
2nd floor 

1st floor 


121,000+ 000,000 

2 

121,000+ 242,000 
2 

242,000+ 363,000 
2 


60,500 ft.-lb. 


181.500 ft.-lb. 

302.500 ft.-lb. 


2,393,000+2,773,000 
2 , 

2,773,000+2,382,000 


= 2.583.000 ft.-lb. 
= 2,577,500 ft.-lb. 







STEEL CONSTRUCTION 


323 


Note that the bending moments in the girders given above are 
for one side only of the column; an equal amount occurs at the other 
side, making the total amount to be resisted at each floor twice that 
given. 

Resistance of Spandrel Girders. Consider now the wind from 
the North or from the South. At all floors resistance is offered by 
the spandrel girders between columns 1-36 and 7-^2 (except at first 
floor 1-36), and by interior and court wall girders in a north and 
south direction. 

In the upper part of the building, the girder sections which are 
required by the gravity loads are sufficient for resisting the wind 
stresses. The first step is to determine the resistance that can be 
developed by these girders and then find at which floor it is neces¬ 
sary to use special construction. The connections of the spandrel 
girders are shown in Plate F and Fig. 190. The horizontal shearing 
value .of the (field) rivets in one flange at 50 per cent excess values 
is 4X.44X 15,000 or 26,400 pounds. Then the resisting moments for 
one end of each beam of various depths are as follows: 


12-inch beam 
15-inch beam 
18-inch beam 

20- inch beam 

21- inch beam 
24-inch beam 


1 X 26,400 = 26,400 ft.-lb. 
UX 26,400 = 33,000 ft.-lb. 
\\X 26,400 = 39,600 ft.-lb. 
1 § X26,400 = 44,000 ft.-lb. 

1 £ X 26,400 = 46,200 ft.-lb. 

2 X 26,400 = 52,S00 ft.-lb. 


This applies to the court spandrels as well as to the outside spandrels. 

Resistance of Interior Girders. The connections of the interior 
girders are shown in Plate I and Fig. 191. In the case where each 
flange is connected by six f-inch rivets, the horizontal shear resist¬ 
ance is 6 X 44X15,000 or 39,600 pounds. Then the resisting moments 
for one end of beams of various depths are as follows: 


12-inch beam 
15-inch beam 
18-inch beam 

20- inch beam 

21- inch beam 
24-inch beam 


1 x 39,600 = 39,600 ft.-lb. 
HX39,600 = 49,500 ft.-lb. 

1 \ X 39,600 = 59,400 ft.-lb. 
1§X39,600 = 66,000 ft.-lb. 
1|X39,600 = 69,300 ft -lb. 

2 X 39,600 = 79,200 ft.-lb. 



C24 


STEEL CONSTRUCTION 


On a typical floor the number of connections and their values are: 

V 


4 spandrel beams 
12 spandrel beams 
18 spandrel beams 


15 inch at 33,000 = 132,000 ft.-lb. 

18 inch at 39,600 = 475,200 ft.-lb. 

21 inch at 46,200 = 831,600 ft.-lb. 1,438,800 


4 interior beams 18 inch at 59,400 = 237,600 ft.-lb. 

14 interior beams 21 inch at 69,300 = 970,200 ft.-lb. 1,207,800 

2,646,600 

This resistance is sufficient at the eighth floor and upward. Above 
the tenth floor the interior connections may be reduced, as indicated 
on Plate I. 


The interior connections cannot be increased without the use 





i . 


-“M 


<>—n 


/•- 2 X 6600 X 1.00 X3%-50600 
2 - 2 X 6600 x .85 X3j-36S00 
3.-2XS625X 72x2^-22300 

4- 2X 5625 X 60 X 24*15 200 

5- 2X 5625X 46X32= 3000 
6 - / x 5625 X .26 X / = /500 

135100 

(C) 


fa) 

Fig. 206. Diagram Showing Method of Computing Resisting Moment of 

Girder Connection 


of brackets which would project through the fireproofing. The 
spandrels are not so limited and brackets can be used to increase 
their resistance. In this manner the resistance to wind stresses can 
be provided down to and including the fourth floor, Fig. 192. 

Girder Resistance for Third Floor. At the third floor, the wall 
construction is such as to make desirable deep spandrel girders 





































STEEL CONSTRUCTION 


325 


between columns 1-8 and 7-42. These girders with their connec¬ 
tions are shown in Plate E. The total amount to be resisted at the 
third floor is 2 x 2,104,000 or 4,208,000 foot-pounds. Of this about 
1,500,000 foot-pounds are resisted by the interior beams, leaving 
2,700,000 foot-pounds to be resisted by the spandrel beams. Con¬ 
sider this divided equally between the two sides, there being 10 
connections on each side, so that each connection in the spandrels 
1-86 and 7-42 must resist 135,000 foot-pounds. This requires brackets 
of the type shown in Fig. 192 for the I-beams 8-86 and the connec¬ 
tions shown for the plate girders, Plate E. 

The computations of the connection of the plate girders are 
shown in Fig. 206; a is the rivet spacing; b is a graphical diagram 
giving the proportions of the full rivet stress for the rivets at various 
distances from the center, and c is the computations. Thus item 1 
is 2 field rivets, f-inch diameter, in single shear, at full unit stress, 
with a moment arm of 3f feet; item 3 is 2 field rivets, j-inch diam¬ 
eter, in single shear, at 0.72 of the full unit stress, with a moment 
arm of 2| feet. The total resistance is somewhat larger than 
required. 

The girder section is excessive, the depth being fixed by the 
spandrel construction, and plates and angles being the minimum 
sizes suitable for this situation. 

Girder Resistance for Second Floor. At the second floor the 
interior girders are arranged differently, so their resistance must be 
computed. The methods just given, applied here give 172,000 foot¬ 
pounds as the bending moment at each spandrel connection. The 
connections to the columns are designed in the manner previously 
illustrated, Plate D. 

Girder Resistance for First Floor. At the first floor there are 
no spandrel girders between columns 1-36. The columns in this 
row are bedded in the basement wall. The wall is assumed to resist 
one-half of the wind stress at this floor. The other half of the stress 
is resisted by the interior girders 20-41 and the spandrel girders 7-42 , 
Plate C. 

The mistake is sometimes made of neglecting the wind bracing 
at the first floor. This is the most important place where it should 
be given attention. It cannot be expected that the pressure will be 
transmitted to the earth at a higher level than the basement floor. 


326 


STEEL CONSTRUCTION 


Proof of Column Sections. It remains to be determined 
whether the column sections are overstressed by adding the w ind stress 
to the gravity stresses. One case serves to illustrate the method. 

At the second floor, the bending moments in column 8, corre 
sponding to those in the connecting spandrel girders, are 160,000 
foot-pounds and 184,000 foot-pounds above and below the floor, 
respectively. Consider the first-story column. This bending mo¬ 
ment is based on a moment arm of 7\ feet. The critical section is 

at the base of the bracket -which is 3 feet below the center of the 

41 

girder. At this point the bending moment is 184,000Xy* or 108,000 

foot-pounds, or 1,296,000 inch-pounds. 

The column section in the first story is 

1 web plate 12" X 

4 Ls 6"X4 "Xf 

6 cover plates 14" X 


The bending is about the axis which is parallel to the web, so the 
values of c and r must be taken in reference to this axis, c is 7 inches, 
one-half of the width of cover plate, and r taken from the tables for 
this column is 3.5. Then the concentric equivalent load is 



1,296,000X7 
3.5X3.5 


740,000# 


The gravity load on this column is 1,088,000 pounds, making 
the total for which it must be designed 1,828,000 pounds. The 
length may be taken at 11 feet on account of the depth of bracket. 
According to the column formula, this section is good for 1,196,000 
pounds. For the combined stress this is increased 50 per cent and 
equals 1,794,000 pounds. As this is within 2 per cent of the required 
capacity, it is accepted. 

The designer is warranted in making liberal assumptions as to 
the lengths of columns and the allowance of excess stress when they 
are built into substantial masonry walls. 

This case illustrates the desirability of carrying as much of the 
wind load as practicable on the interior columns and girders, other¬ 
wise the exterior columns may need to be increased above the re¬ 
quirements of the gravity loads in order to take the heavy wind 
stresses. * 



STEEL CONSTRUCTION 


327 


In cases like that above, it may be best to turn the columns in 
the other direction. It is simply a question whether the effect of 
the wind stress is more important than the effect of the eccentric 
gravity loads. 

Other Wind Stresses. Now, consider the wind from the East 
or from the West. It happens that the south wall of the building 
is solid, so that, diagonal bracing can be used, as shown in Plate I, 
and such bracing is designed to take one-half of the wind stress in this 
direction. At the ninth floor a strut extends across the court so that 
the two sets of bracing co-operate below that level. The other half of 
the wind stress is carried by the interior east and west girders and 
the spandrel girders 1-7. The problems involved do not differ 
from those that have been described. 

MISCELLANEOUS FEATURES 

Chimney and Its Supports. The chimney, Plates H and I, is 
located near column 31. It extends from the sub-basement floor 
to the top of the penthouse. It is made of steel plates. The thick¬ 
ness of plates is arbitrary, the chief consideration being durability. 
The chimney is lined inside with an insulating material which is 
supported by shelf angles spaced 3 feet apart. The chimney is 
designed to be built in sections corresponding to the two-story 
column lengths. The sections are joined together by means of 
flange angles and bolts. 

The entire weight of the chimney must be carried from one 
support, as its length varies with changes in temperature. So far 
as the finished structure is concerned, it could rest on the sub-base¬ 
ment floor, but for convenience in erection it is supported at the 
first floor. Thus it can be erected along with the structural steel, 
the basement and sub-basement sections being placed at any con¬ 
venient time afterward. Usually the sub-basement work is not 
done until after the steel framework is erected and it would then be 
difficult to get the chimney into place. 

The details of the breeching connection are given to control 
both the structural steel fabricator and the builder of the breeching. 

Masonry Supports. Along the two facades at the first floor 
are some granite bases which require supports. These supports, 
detailed in Plate C, are made independent of the sidewalk construe- 


328 


STEEL CONSTRUCTION 


tion so that the granite can be set in advance of building the side¬ 
walk and also so it will not be affected by any possible settlement 
of the sidewalk. 

At all floor levels or other convenient points, provision must be 
made for supporting the masonry across the face of the columns. 
This can be done on this building in most cases by extending a part 
of the spandrel sections across the column. But in many buildings 
special shelves must be built. 

Lintels. Most of the spandrel girders are so located that they 
serve as lintels over the windows. Plates are riveted on the bottom 
flange over these openings to support the outer course of bricks or 
the terra cotta lintel. The edge of the plate is placed 2 inches back 
from the outer face of the brickw’ork. Some designers prefer to 
extend these plates the entire length of the girder to support the 
face brick, Plates L and T. When the windows are not high enough 
for the above lintel detail, detached angle lintels are used. 

Spandrel Sections. On buildings having elaborate facades, 
many special details must be designed for supporting the masonry. 
The spandrel sections on this building, Plates L and T, are com¬ 
paratively simple. 

At the second floor a projecting plate is used along the bottom 
flange of the girder. At the third floor a similar plate is used and, 
at the top of the girder, brackets project out for supporting a belt 
course of terra cotta. 

Ornamental metal balconies at the seventh, ninth, eleventh, 
and thirteenth floors are supported by light angle brackets riveted 
to the girders. 

A terra cotta balcony at the fifteenth floor requires the special 
framing shown for it. 

In general, wherever terra cotta is used, anchor holes are re¬ 
quired in the structural steel. It is the duty of the designer to 
secure the necessary data and put it on the drawings. These holes 
usually are spaced about six inches apart horizontally. Only the 
vertical dimensions need be supplied. 

The cornice support is quite similar to that of the terra cotta 
course at the third floor. For wide cornices, brackets project from 
the columns, and these brackets carry beams for the support of the 
terra cotta. Every case requires its special design. 


STEEL CONSTRUCTION 


329 


Flag Pole Support. Near column 7 on the roof plan, Plate G, 
is shown a pair of channels for supporting a flag pole. A similar 
pair of channels occurs at the attic floor. On some buildings the 
flag pole can be connected directly to a column. This is the simplest 
and most desirable scheme. In some cases it may be set in sockets 
on the roof and braced with angle or other struts. 

No data are known to the writer regarding the load on a flag 
pole. A load of 20 pounds per square foot applied to the area of the 
flag seems sufficient to cover the actual wind pressure and vibration. 

Mullions. Where the space between windows is not enough to 
permit a substantial masonry pier, the mullion should be reinforced. 
I-beams, tees, or angles may be used, depending on the conditions. 
In this case two rods are built into the brickwork, Plate L. 

Anchors. The anchor rods shown extending through the span¬ 
drel girders and into the concrete slab hold the spandrel girders 
laterally and make a rigid connection between the framework and the 
floor construction, Plate L. 

DIMENSIONING DRAWINGS 

Base Lines. The base lines for horizontal dimensions are the 
building lines of the structure. They are shown on the first-floor 
plan, Plate C. The building lines nominally represent the outside 
lines of the building walls. In reality they are often imaginary 
reference lines, for, on account of the offsets, parts of the wall may 
extend beyond these lines and other parts be inside of them. For 
the class of buildings under consideration, the building lines usually 
coincide with the lot lines. If they do not, then the lot lines should 
be shown and dimensioned from the building lines. If the corners 
of the building are not exactly right angles, the angles must be 
marked on the first-floor plan. The cardinal points of the compass 
should be marked with approximate accuracy on the first-floor plan. 
One of these points is used as a reference in marking one side of 
columns and one end of girders for convenience in erecting; thus 
E on the east face of a column, or N on the north end of a girder. 

Column Centers. Having established the building lines, the 
next step is to dimension the column centers. The simplest situa¬ 
tion is had when the building is rectangular and the columns are in 
rows in both directions. Then two lines of dimensions will suffice 



330’ STEEL CONSTRUCTION 

to fix the location of all columns, Plate D. Any irregularity of 
spacing in any row requires a special line of dimensions in that row. 


Pig. 207. Diagram Showing Method of Dimensioning Column Centers in an Irregular Building 


With arr irregularly shaped building, the dimensioning becomes 
more complicated. One building line should be adopted as a refer¬ 
ence line, taking the one to which the greatest number of column 
lines are perpendicular and parallel. Then all columns should be 
located by dimension lines perpendicular and parallel to this refer¬ 
ence line, that is, by rectangular co-ordinates. The only diagonal 

dimensions needed are those along which, 
or parallel to which, steel members are 
placed. 

In Fig. 207, the reference line used 
is the south building line. The building 
lines in this case are probably lot lines. 
Their lengths and the angles are de¬ 
termined by a survey. The distance 
from the lot lines to the column centers 
is established at l'-lO" on all sides. The 
^ ^. . spacing of columns 1 to 7 and the ar- 

Fig. 208. Construction Diagram for “ ® 

Details of Figure 207 rangement of the other columns are fixed 

by architectural conditions. 

From the foregoing data all the required dimensions can be 
computed by trigonometry. First, compute the distances from 


zs 



































STEEL CONSTRUCTION 


331 


column 7 to the corner of the building. From Fig. 208 it is apparent 
that these distances a b and a'b are equal to each other and equal to 
caXcot 41° 15'; then 

a b = a'b — 22" X1.140 = 25 T V' 

The distance between columns 9 and 15 is 

20'-0"Xtan 19° 20" = 20'-0" X .3508 = 7'-0 
In this manner all the dimensions can be computed. 

Problem 

Compute the distances between columns which are lacking in Fig. 207. 

The column center dimensions should be repeated on all the 
floor plans. If the floor framing plan is crowded, a separate diagram 
at small scale may be placed on the drawing to display the column 
center distar ces. 

Girders and Joists. Girders and joists are dimensioned from 
the column centers. The dimension lines required are illustrated 
in Figs* 201 and 202. Note in Fig. 201-b that there is no joist at 
column 23, so the space is divided and the adjacent joists tied in 
the column. No dimensions are required for the lengths of joists 
and girders other than those locating the centers of the columns 
and beams to which they connect. The shop detailer computes 
the actual lengths of beams required. But if one end of a beam 
rests on a wall, one face of the wall and its thickness must be given. 

Such details as struts, mullions, plates for supporting brick¬ 
work, etc., are also located from column centers, as illustrated on 
the floor plans. 

Vertical Dimensions. The vertical dimensions from floor to 
floor are given in a separate diagram or in connection with the 
column schedule, Plate H. At the first floor a reference is made to 
established sidewalk grade in terms of its elevation above datum, 
Plate C. The elevations of beams are given in reference to the fin¬ 
ished floor elevations, respectively. Usually the elevation of joists 
and girders can be covered by a note, Plate F. Special cases can 
be given by figures alongside the beams indicating the distance 
from the floor level to the top flange of the beam; thus — 5\" means 
thait the top flange is 5| inches below the floor line. 

Elevations of Spandrel Beams. The elevations of spandrel 
beams can be shown best on the sections, where both the elevation 


332 


STEEL CONSTRUCTION 


and the horizontal position can be given in relation to the other 
materials of construction thereabout, Plate L. 

Summary. The use of unnecessary dimensions and needless 
repetitions may be a source of much inconvenience. It increases 
the probability of errors and causes extra work in checking. 

While structural steel drawings should be made reasonably 
accurate to scale, scaled dimensions must not be used in executing 
the work. 

The scales used in making drawings of structural steel should 
be as follows: for framing plans, J inch or \ inch; for spandrel sec¬ 
tions, \ inch or f inch; and for details showing all dimensions and 
rivet spacing, 1 inch or 1^ inches. In each case the scale first given 
is preferred. The use of a number of different scales in the same 
set of drawings is objectionable. 






UNIVERSITY CLUB AND MONROE BUILDING, CHICAGO 
Holabird & Roche, Architects 

























STEEL CONSTRUCTION 

PART V 


PROTECTION OF STEEL 

PROTECTION FROM RUST 

Rust. Although steel is the strongest of building materials, 
under unfavorable conditions it may be one of th east durable. Its 
great enemy is rust. The corrosion or rusting of iron and steel is 
familiar to every one. It is a chemical change in which the metallic 
iron unites with oxygen and forms oxide of iron or rust. 

RUST FORMATION 

Theory. While rust is largely or wholly oxide of iron, it is not 
produced directly by the contact of the iron with the oxygen of the 
air. The presence of moisture seems essential to its formation. 
Much study has been given to the process of rust formation, but the 
reactions have not yet been determined positively. It is quite 
generally believed that electrolytic action occurs. This theory is 
well described by Houston Lowe in “Paints for Steel Structures” 
as follows:* 

“The electrolytic theory, which no doubt has the strongest support, is 
based upon the recognized tendency of metals to go into solution, even in pure 
water. The act is accompanied by the release of hydrogen positively charged 
with electricity, leaving on the metal a corresponding charge of negative elec¬ 
tricity. If oxygen is at hand to combine with the hydrogen, the electrical 
tension is relieved in an infinitely small current and new portions of the metal 
pass into solution; otherwise the action is arrested by the non-conducting quality 
of the thin film of hydrogen. 

“The presence of minute particles of suitable impurities in or on the iron, 
whose solution tension differs from the iron, or the presence of acids in the water, 
facilitates the discharge of the electric tension and, hence, the continuous re¬ 
moval of particles of iron On the other hand, the presence of alkalies, and a few 
other substances that decrease hydrogen ion concentration, will diminish or 
even stop iron solution and rusting altogether. 

“This, in brief, is the substance of the electrolytic theory of rusting, the 

♦John Wiley & Sons, Publishers. New York. 




334 


STEEL CONSTRUCTION 


more complete explanation of which would involve the details and language of 
the ionic theory of chemical action. Corrosion of iron, in the sense in which 
that term has been used in this section, has nothing whatever to do with elec¬ 
trolysis by stray electrical currents from outside sources. The currents involved 
in rusting under the theory of electrolytic action are almost infinitely short and 
minute, a d originate in or on the metal itself. 

“The theory is valuable to the extent that it suggests reasonable and 
practical remedy of the defects either of the metal or its proposed covering, or 
both. As in the treatment of diseased animal and plant tissues, so in this case, 
intelligent diagnosis must precede the application of preventives of rust. Ex¬ 
perimental work following the lines of the electrolytic theory in seeking, first, 
to prevent, or ‘inhibit’ corrosion by a priming coat and, secondly, to diminish 
the penetration of water by suitable overcoats, is promising good results, and a 
final solution of the problem is confidently looked for. 

“The tendency of rust to grow and spread out from a center has an adequate 
explanation in the electrolytic theory. This phenomenon is especially per¬ 
nicious, as it results in pitting or, under a paint coat, in a growth which finally 
flakes off the paint and exposes large areas of the iron.” 

Degrees of Exposure. A piece of steel exposed to the air will 
ultimately change entirely to oxide of iron (except as to the contents 
other than pure iron) i. e., it will be entirely destroyed by rusting. 
The rapidity of the change varies with the conditions of exposure. 
The rusting will proceed very slowly if the steel is kept in dry air; 
less slowly if subjected occasionally to moist air; rapidly if exposed 
to moisture frequently; and very rapidly if exposed to moisture in 
the presence of sulphur or other acid fumes. 

The first condition prevails when steel is enclosed in other 
materials of construction, as columns and beams enclosed by plaster 
in partitions, and in floor construction, so that the moisture condi¬ 
tions change only slightly. The second condition applies when the 
steel is within the building, but not encased in other materials, thus 
being exposed to varying degrees of moisture, as unprotected col¬ 
umns and beams in storerooms. The third degree of exposure 
fairly represents unprotected beams in basements, vaults under 
sidewalks, and steel work out of doors. And the worst possible 
exposure, that is, to moisture in the presence of acid fumes, is had 
in smelters, and in structures where the steel is subjected to the 
smoke from railroad locomotives. 

Rate of Rusting. Some studies have been made of the rate 
of corrosion under different conditions. It is very evident that the 
rate varies greatly with the conditions of exposure. Experiments 
along this line have not gone far enough to give conclusive results, 


STEEL CONSTRUCTION 


335 


i. e., definite figures as to the thickness of metal that will change to 
rust in a given time. But it is a matter of common knowledge that 
there is enough rusting even under the most favorable conditions to 
make it important that steel be protected. 

Effect of Composition of Metal. The composition of the 
metal has some effect on the rate of corrosion. Structural steel 
probably rusts more rapidly than any other form or alloy of iron. 
Cast iron rusts slowly, probably due to the presence of graphite, 
which protects the iron. Wrought iron rusts more rapidly than 
cast iron and much less rapidly than steel. It is believed that the 
slag in wrought iron protects the fibers of iron from exposure to the 
air and moisture. The presence of manganese is supposed to accel¬ 
erate corrosion, while copper and other alloys retard it. 

Efforts have been made to produce rust-resisting metals by 
two methods; by making iron nearly pure, and by using an alloy 
of copper. The resulting metals are not rustproof but show much 
slower rates of corrosion than ordinary steel. Both have been 
commercially successful as applied to sheet steel, but are not yet 
used for structural steel. Pure iron is not suitable for structural 
purposes because of its lack of strength. It is quite possible that 
an alloy of copper or other metal will be developed for structural 
steel that will be nearly rustproof. 

PAINT 

Purpose. The usual means employed to prevent corrosion is 
to exclude all air and moisture from contact with the metal by a 
covering of paint. It is desirable that the paint material be such 
as will inhibit the formation of rust, thus counteracting any imper¬ 
fections of the paint in excluding moisture. 

Qualities. The following qualities are desirable: 

(1) Adhesive, so that it will hold fast to the steel. 

(2) Non-porous, so that it will exclude air and moisture. 

(3) Elastic, so that it will not crack with changes in tempera¬ 
ture, or with the deflection of the steel. 

(4) Hard at all ordinary temperatures. 

(5) Non-volatile, so that the oils may not evaporate and leave 
the inert materials of the paint without a binder. 

(6) Not soluble in water. 

(7) Not soluble in oil, so that it will not soften when addi¬ 
tional coats are applied. 


336 


STEEL CONSTRUCTION 


(8) Inhibitive, that is, of such material as will prevent the chem¬ 
ical or electrolytic action of rusting. 

(9) Color may be important. 

Many of these qualities obviously are much more important 
on out-of-door work than on ordinary building work. No paint 
has all of these desirable qualities, but by using different paints for 
the several coats, the ideal condiiions may be approximated. Thus 
the first coat should be inhibitive and adhesive; and the second (or 
last coat, if more than two are used) shouLd be non-porous and 
should provide the required wearing properties. 

Composition. A paint is made of a liquid and a solid, called, 
respectively, the “vehicle” and the “pigment”. 

Vehicle. The best vehicle for paint is linseed oil. It may be 
had as raw oil or boiled oil. The latter is used when quick drying 
is desired but the raw oil is believed to give better results under 
most circumstances, and especially with red lead. The drying of 
paint is accelerated by the use of driers in the oil. A drier may be 
a volatile oil, as turpentine, which effects its purpose by rapidly 
evaporating after the paint is applied; or it may be a japan, which 
hastens the hardening of the oil and pigment. Turpentine being 
cheaper, it is more used than japans. The drier should not exceed 
8 per cent of the vehicle. 

Linseed oil varies greatly in quality even when pure, and is 
subject to adulterations which are difficult to detect. Some paint 
makers claim, and probably justly so, that they improve the vehicle 
by adding other oils to the linseed oil; but in generabany additions 
other than the drier must be considered adulterations. 

Pigments. Pigments commonly used for structural steel paints 
are red lead, iron oxide, graphite, and lampblack. 

Red lead is the red oxide of lead, Pb 3 0 4 , but the red lead of 
commerce contains a certain amount of litharge and metallic lead. 
These elements cannot be entirely eliminated on a commercial .basis, 
but it is practicable to obtain a red lead which is 95 per cent pure 
and it should be so specified. 

When mixed with linseed oil, red lead hardens, much as cement 
when mixed with water, and forms a strong tenacious coating. It 
can be made into a heavy paint, almost a paste, thus giving a heavy 
coat on the steel, or it can be thinned to give a light coat. On 


STEEL CONSTRUCTION 


337 


account of its weight, red lead is difficult to mix with oil. This is 
especially true when a large proportion of lead is used. The maxi¬ 
mum proportion is 33 pounds of red lead to one gallon of raw linseed 
oil. While this heavy mixture is desirable, it is expensive as to 
labor and materials. A more practicable proportion is 25 pounds 
of red lead to one gallon of oil; a still smaller weight of lead is often 
used and will invariably be used unless the proportions required 
are definitely specified, for there is no standard practice to govern 
it. Red lead paint with a small proportion of red lead can be mixed 
by hand, but if the amount of lead is as much as 25 pounds, the 
mixing should be done in a churn, or ground into the oil at the paint 
factory. 

On account of its weight and its settling qualities, it has not 
been practicable, heretofore, to keep red lead paint for any length of 
time, as the lead settles to the bottom and hardens. The hardening 
quality seems to be due largely to the litharge. Now that the lith¬ 
arge can be eliminated from the red lead, it is practicable to keep 
the ready-mixed paint for a much longer period. It can now be 
obtained from the paint manufacturers ground into the oil, forming 
a thick paste, which can be thinned to the proper consistency by 
the addition of oil when it is to be used. The thinning can be 
gaged by the weight of the finished paint on the following basis: 

A weight of 24.43 pounds for the finished paint corresponds to 
25 pounds of lead to one gallon of oil. 

A weight of 25.92 pounds corresponds to 28 pounds of lead to 
one gallon of oil. 

A weight of 26.76 pounds corresponds to 30 pounds of lead to 
one gallon of oil. 

A weight of 27.10 pounds corresponds to 33 pounds of lead to 
one gallon of oil. (These values are taken from a circular issued by 
the National Lead Company.). 

A ready-mixed red lead paint can be made by substituting for 
a part of the red lead some other pigment of inert material which 
will retard the settling, and harden. Lampblack, asbestine, and 
mica are sometimes used for this purpose. Such paints usually 
contain less than 15 pounds of red lead per gallon of oil, and are 
much less satisfactory than the red lead paste. 

Iron oxide, commercially available, varies greatly in weight and 
physical characteristics. Some is taken direct from mines but most 


338 


STEEL CONSTRUCTION 


of it is manufactured. It does not have any cementing properties 
when mixed with linseed oil so must be held in place by the oil. 
The paint will last only as long as the oil binder remains intact. 
The iron oxide does not inhibit corrosion but under some circum¬ 
stances accelerates it, .thus leading to the formation of patches of 
rust under the paint. Under favorable conditions it makes a good 
protective coating. Iron oxide is mixed with boiled linseed oil, 
using about 8 pounds of the pigment to one gallon of oil. 

The carbon paints, which include lampblack and graphite, have 
no cementing properties when mixed with oil. The amount of 
pigment used is small compared with that used in red lead paint. 
It, therefore, has much greater spreading power and consequently 
makes a much thinner film. As it does not inhibit corrosion, its 
protective power depends entirely on the oil, making it necessary to 
use several coats in order to get satisfactory results. It makes a 
satisfactory second coat over red lead. The carbon pigments, 
particularly graphite, are subject to many adulterations. There are 
no standard proportions. Carbon paints can be made at the factory 
and will keep for an indefinite period. 

Prepared Paints. Many proprietary paints are offered for 
structural steel. Some have much merit, others none. They should 
not be used unless there are authentic records of successful use. 

Painting Required. Structural steel in buildings is protected 
from moisture by being enclosed by other materials. On the other 
hand, in most cases it cannot be repainted, so the original painting 
is of great importance. The writer recommends painting it two 
coats, first red lead, second graphite or lampblack. If the steel is 
to be encased in concrete, the second coat may be omitted, the con¬ 
crete furnishing as much protection as the second coat of paint. 

Cleaning. The paint can have no mechanical bond to the 
steel so must depend on adhesion to hold it in place. This makes it 
necessary that the surfaces be cleaned before painting, removing all 
rust, dirt, grease, and mill scale. The cleaning is of utmost impor¬ 
tance, for if not done thoroughly, the paint will not adhere; and, if 
rusting has already started, it may continue under the paint. It 
is not uncommon to find large patches of rust over which the paint 
remains unbroken. This is apt to occur when the surface is not 
properly cleaned before repainting. 


STEEL CONSTRUCTION 


339 


The most effective way of cleaning steel is by means of the 
sand blast. This method is expensive and is not much used for 
steel work for buildings. It is used chiefly for cleaning old steel 
work, especially bridges, for repainting. The usual means of cleaning 
is by the use of the scraper, chisel, and wire brush. This work can 
be well done with these tools, if enough labor is expended on it. 

Applying the Paint. The paint is best applied with heavy 
round brushes. It must be spread evenly and cover the entire 
surface and be worked into all corners and joints. The metal surfaces 
should be warm and free from moisture. In cold weather the paint 
should be warmed. 

Surfaces in Contact. It is customary to specify that surfaces 
which will be in contact after assembling shall be painted before 
assembling. The desirability of this has been questioned on the 
basis that the paint is probably destroyed by the heat from the 
rivets. Nevertheless, there is no evidence that such painting does 
any harm and it is best to do it in accordance with usual practice. 
Box sections, such as channel columns, should have two coats on 
the inner surfaces before assembling. 

Cement as a Rust Preventive. Portland cement mortar and 
concrete are inhibitors of rust and, if dense and in actual contact 
with the metal, provide the necessary protection against moisture. 
If applied to clean steel surfaces, no other protection is required. 
But the steel, if not painted at the shop, usually will become badly 
rusted before it is enclosed in the building, making it desirable that 
the shop coat of paint be used. Then the concrete casing will 
make it unnecessary to apply the second coat of paint. 


PROTECTION FROM FIRE 

Effects of Heat on Steel. Expansion. Heat applied to steel 
causes it to expand. Its coefficient of expansion is 0.0000067 for 
one degree Fahrenheit, that is, for each increase of one degree in 
temperature a unit of length increases by the amount of the coeffi¬ 
cient. Thus for an increase of 100 degrees in temperature, the 
increase for each unit of length is 100X0.0000067 = 0.00067; for a 
length of 18 feet, the total increase in length is 0.00067X18 = 
0.01206 feet, or .14472 inches. 


340 


STEEL CONSTRUCTION 


There is a corresponding change in the opposite direction, if 
the temperature decreases. From this it is clear that expansion and 
contraction due to changes in temperature occur in appreciable 
amount. The longer the member, or series of members, the greater 
the change in length. Within buildings, the change in temperature 
ordinarily is not enough to cause trouble, but if the steel is exposed 
to fire, it might expand enough to push a wall out of place even 
though not heated enough to affect its strength. Cases have occurred 
where walls have been seriously displaced by ordinary changes of 
temperature, because the expansion of the steel pushed the wall 
outward, whereas the succeeding contraction did not pull it back; 
then the next, expansion pushed it farther out, and thus by succes¬ 
sive movements the wall was pushed farther and farther out of place. 

Loss of Strength. Experiments indicate that steel can be heated 
to a temperature of about GOO degrees Fahrenheit before it begins 
to lose strength. At higher temperatures, it loses strength rapidly 
and will fail of its own weight at a temperature of about 1500 de¬ 
grees. Steel melts at 2500 degrees (approx.). 

Intensity of Heat in a Fire. The intensity of heat developed 
in a fire varies greatly according to conditions. Many cases are 
recorded showing steel bent into a tangled mass from the burning 
of a building, indicating temperatures of 1500 degrees or more. 
Such temperatures can be produced by burning the wood framework 
of an ordinary building, or even the contents of a fireproof building. 

Protective Methods. Unprotected steel yields very quickly in 
a fire, much more quickly than wood beams of the same strength. 
It is dangerous and inexcusable to use structural steel in a building 
without providing for its safety. Steel is protected from fire by 
encasing it in a fireproof material. Almost any material encasing 
steel will protect it to some extent. Even a tight casing of wood 
will protect it for a little while in a fire. Ordinary plaster on wood 
lath will protect it only until the fire gets through the plaster, after 
which the burning of the lath aids in the destruction of the steel. 
Cement plaster on metal lath is efficient only to a limited degree, 
and while it is an incombustible material, it is not fireproof within 
the meaning of that term as used in building construction. 

Misuse of the Term Fireproof. Many buildings are called fire¬ 
proof when the protection of the steel is nothing more than described 


STEEL CONSTRUCTION 


341 


above. Instances can be cited of hotels advertised as fireproof with 
steel beams placed among wood joists with no protection whatever. 

Amount of Protection Depends on Conditions . A building may 
be made entirely of incombustible material and still not be fireproof, 
if the steel is not encased to protect it from the contents of the 



BRICK ARCH CONSTRUCT!OR 
Fig. 209. Brick and Concrete Arch Construction Showing Partial 
Protection for I-Beams 

building. Fig. 209 illustrates a form of construction of this sort 
which was much used a number of years ago. The brick arches 
and the concrete filling protect the beam except on the bottom 
flange, which is left exposed to fire from the burning of the contents 
of the room below'. Fig. 210 is a similar form of construction in 
which a corrugated-steel arch replaces the brick arch. This partial 
protection is of some value, but it is so easy under present methods 
to get complete protection that these forms are no longer used. 

On the other hand, a building having no combustible material 



COR RUGA TED IRON ARCH CONSTRUCTION 


Fig. 210. Corrugated Iron and Concrete Arch Construction Showing 
Insufficient Protection for I-Beams 


in its construction or con-tents, and having no external hazard, need 
not have its steel framework fireproofed. A foundry building or a 
machine shop may be such a case. 

Standard Specifications. Steel to be really fireproofed must be 
entirely encased in a fireproof material. 1 he material must be 
such that it will conduct heat very slowly and that it will maintain 
its integrity when subjected to a fire of the greatest in tensity and 
longest duration likely to occur, and when subjected to a stream of 
water from a fire hose while at its maximum heat. 

The “Standard Test for Fireproof Floor Construction” adopted 
by the American Society for lesting Alaterials requires. 

•American Society for Testing Materials, Edgar Marburg, Secretary, University of Penn¬ 
sylvania, Philadelphia. 



















342 


STEEL CONSTRUCTION 


“No plastering shall be applied to the underside of the floor construction 
under test. 

“The floor shall be subjected for four hours to the continuous heat of a fire 
of an average temperature of not less than 1700° F., the fuel used being either 
wood or gas, so introduced as to cause an even distribution of heat throughout 
the test structure. 

“The heat obtained shall be measured by means of standard pyrometers, 
under the direction of an experienced person. The type of pyrometer is immater¬ 
ial so long as its accuracy is secured by proper standardization. The heat 
should be measured at not less than two points when the main floor span is not 
more than 10 feet and one additional point when it exceeds 10 feet. Tempera¬ 
ture readings at each point are to be taken every three minutes. The heat 
determination shall be made at points directly beneath the floor so as to secure 
a fair average. 

“At the end of the heat test a stream of water shall be directed against the 
underside of the floor, discharged through a lj-inch nozzle, being held at more 
than 3 feet from the firing door during the application of the water.’* 

Material which will withstand this test is suitable for fireproofing 
steel in any part of a building. 

Fireproof Materials. Cinder Concrete. Cinder concrete has 
been used extensively for fireproofing but it is not altogether satis¬ 
factory. It is difficult to get cinders free from unburned coal, 
ashes, and refuse. Sulphur in the cinders causes rusting of the 
steel. Its use is not warranted on first-class work. 

Portland Cement Concrete. Portland cement concrete, made 
of crushed stone or gravel, is an excellent fireproofing material. It 
has the necessary resistance to fire and water, prevents rusting of 
the steel, and in many situations adds to the strength of the steel 
member. If its surface is left rough or is roughened after the 
forms are removed, plaster will stick to it. 

When subjected to a fire, the concrete is damaged. The depth 
of the injury may be as much as 1| inches, depending on the quality 
of the concrete and the kind of stone used in it. The better the 
concrete, the less it is injured by the heat. Heat calcines limestone 
and disintegrates granite, so that these stones are not as suitable 
for fireproofing purposes as hard sandstones, trap, and other stones 
not so easily affected by heat. An excellent concrete for fireproofing 
can be made from crushed tile and brick. On buildings where tile 
is used for floor arches and partitions, the broken pieces can be 
crushed and used for fireproofing the columns and any other mem¬ 
bers not protected by the tile floor arches. 


STEEL CONSTRUCTION 


343 


Concrete which has been damaged by fire does not lose its 
property of non-conductivity, consequently it is efficient as fire¬ 
proofing so long as it remains in place; although it has lost its 
strength, it usually will remain in place until removed by some me¬ 
chanical means, as the application of a stream of water. After a 
fire, the damaged concrete must be removed and replaced. 

Concrete is placed around steel by building forms around the 
members and pouring concrete into them, Fig. 211. Wire mesh or 
expanded metal should be attached to the bottom flanges of beams 
and wrapped around columns to provide a mechanical bond for the 
concrete so that it will not fall off during or after a fire. 



Fig. 211. I-Beam and Column Sections Showing Concrete Fireproofing. 


Holloiv Tile. Hollow tile is molded from clay and baked at a 
high temperature. The clay used must be such that it will not 
warp, or fuse in the kiln. It is desirable that the tile be porous and 
tough rather than dense and brittle. The tile is made porous by 
mixing sawdust with the clay. This burns out during the baking, 
leaving voids and producing the desired porosity. Dense tile and 
tile which is glazed is likely to shatter, if exposed to a stream of 
water when hot, thus making it useless for fire protection; further¬ 
more, plaster does not adhere to it as well as to porous tile. 

The tile is made hollow to save weight, and to provide air 
spaces which are insulators against both heat and moisture. 

This material is molded into a great variety of shapes to suit 
the various requirements of the steel members to be protected. 
Certain shapes are practically standard; special shapes can be had 
only when required in large quantity. 

Figs. 212, 213, 214, and 215 show a number of illustrations of 
tile fireproofing of joists, girders, spandrels, and columns. The 










344 


STEEL CONSTRUCTION 


joists are usually fireproofed by the skewbacks of the floor arches. 
On other members the tile serves only for fireproofing and for furnish- 




Fig. 212. Method of Fireproofiing Joists in Connection with Flat Tile Floor Arch 


ing a surface for plastering. It can be used for fireproofing steel 
members in almost any situation. 

Tile is set in mortar in the same manner as bricks are laid. 
Any space between the tile and the steel should be filled with Port- 





Fig. 


213. Sections Showing Method of Fireproofing Beams 


land cement mortar. A heavy layer of mortar should be plastered 
on the webs of beams before setting skewbacks or other tiles against 
them. 




































































































































































































































































346 


STEEL CONSTRUCTION 


Fireproofing tile must be designed to be securely supported by 
the steel. Steel clips or wire must be used in some situations. 
Thus the column casing should be held in place by copper wire 
bands unless it is securely held by interlocking of the tile. Soffit 
tile on joists and girders require metal clips or woven wire fabric to 
hold them in place even though they appear to have support from 
shoe tile or other adjacent members. 

Tile has considerable strength in compression and may be so 
used, but should not be subjected to other stresses. 

Brick. Brick masonry is an excellent fireproofing material so 
far as its resistance to heat is concerned. However, it is not easily 


fig 

§§S| 

M 





Fig. 215. Sections Showing Method of Fireproofing Columns with Tile and Concrete 

supported and, therefore, is not generally available for this purpose 
on beams, but in some cases it can be used to good advantage for 
encasing columns. 

Selection of Fireproofing. Portland cement concrete and hollow 
tile are the materials best suited for fireproofing. Both are efficient 
for this purpose. The choice between them is usually governed 
by other considerations, chief of which is the type of floor construe* 
tion, which in turn may be determined by cost or some other con¬ 
sideration. If the floor is to be of reinforced concrete, concrete will 
be used for fireproofing the steel framework. If the floor is to be of 
tile arch construction, that material will be used for fireproofing; 
but even in this case concrete can be used advantageously for the 
columns. 

Thickness of Fireproofing. The thickness of the covering 
required to furnish the desired protection varies with the situation 
and the importance of the member. Columns being vital to the 
support of the building are given the most protection. Lintels and 
spandrel girders are subject to severe exposure and are given about 












































STEEL CONSTRUCTION 


347 


the same protection as columns. Joists and girders are local mem¬ 
bers and not so heavily fireproofed. The top flanges of beams and 
girders do not need as much protection as the bottom flanges. 

The requirements in Chicago are:* 

Columns—Exterior, (a) All iron or steel used as vertical supporting 
members of the external construct ion of any building exceeding fifty feet in height 
shall be protected against the effects of external change of temperature and of 
fire by a covering of fireproof material consisting of at least four inches of brick, 
hollow terra cotta, concrete, burnt clay tiles, or of a combination of any two of 
these materials, provided that their combined thickness is not less than four 
inches. The distance of the extreme projection of the metal, where such metal 
projects beyond the face of the column, shall be not less than two inches from the 
face of the fireproofing; provided, that the inner side of exterior columns shall be 
fireproofed as hereafter required for interior columns. 

(b) Where stone or other incombustible material not of the type defined 
in this ordinance as fireproof material is used for the exterior facing of a building, 
the distance between the back of the facing and the extreme projection of the 
metal of the column proper shall be at least two inches, and the intervening 
space shall be filled with.one of the fireproof materials. 

(c) In all cases, the brick, burnt clay, tile, or terra cotta, if used as a fire¬ 
proof covering, shall be bedded in cement mortar close up to the iron or steel 
members, and all joints shall be made full and solid. 

Columns—Interior, (a) Covering of interior columns shall consist of 
one or more of the fireproof materials herein described. 

(b) If such covering is of brick it shall be not less than four inches thick; 
if of concrete, not less than three inches thick; if of burnt clay tile, such covering 
shall be in two consecutive layers, each not less than two inches thick, each 
having one air space of not less than one-half inch, and in no such burnt clay tile 
shall the burnt clay be less than five-eighths of an inch thick; or if of porous clay 
solid tiles, it shall consist of at least two consecutive layers, each not less than 
two inches thick; or if constituted of a combination of any two of these materials, 
one-half of the total thickness required for each of the materials shall be applied, 
p-ovided t hat if concrete is used for such layer it shall not be less than two inches 
thick 

(c) In the case of columns having an “H” shaped cross section or ot 
columns having any other cross section with channels or chases open from base 
plates to cap plates on one or more sides of the columns, then the thickness of 
the fireproof covering may be reduced to two and one-half inches, measuring 
in the direction in which the flange or flanges project, and provided that the 
thin edge in the projecting flange or arms of the cross sections does not exceed 
three-quarters of an inch in thickness. The thickness of the fireproof covering 
on all surfaces measuring more than three-quarters of an inch wide and measur¬ 
ing in a direction perpendicular to such Surfaces shall be not less than that 
specified for interior columns in the beginning of this section, and all spaces, 
including channels or chases between the fireproof covering and the metal of 
the columns, shall be filled solid with fireproof material. Lattice or other open 
columns shall be completely filled with approved cement concrete. 


♦Revised Building Ordinances of the City of Chicago as amended Feb. 20, 1911. 



348 


STEEL CONSTRUCTION 


Columns—Wiring Clay Tile On. (a) Burnt clay tilexolumn covering 
shall be secured by winding wire around the columns after the tile has all been 
set around such columns. The wire shall be securely wound around tile in such 
manner that every tile is crossed at least once by a wire. If iron or steel wire is 
used it shall be galvanized and no wire used shall be less than number twelve 

gage *** ***** 


Pipes Enclosed by Covering, (a) Pipes shall not be enclosed in the fire¬ 
proofing of columns or in the fireproofing of other structural members of any 
fireproof building; provided, however, gas or electric light conduits not exceeding 
one inch diameter may be inserted in the outer three-fourths inch of .the fire¬ 
proofing of such structural member, where such fireproofing is entirely composed 
of concrete. 

(b) Pipes or conduits may rest upon the tops of the steel floor beams or 
girders, provided they are imbedded in cinder concrete to which slaked lime 
equal to five per cent of the volume of concrete has been added before mixing 
or their being imbedded in stone concrete. 


******** 


Spandrel Beams, Girders, Lintels. The metal of the exterior side of the 
spandrel beams or spandrel girders of exterior walls, or lintels of exterior walls, 
which support a part of exterior walls, shall be covered in the same manner, and 
with the same material as specified for the exterior columns in this chapter; 
provided, however, that shelf angles connected to girders by brackets or pro¬ 
jections of girder flanges not figured as part of the flange section may come 
within two inches of the face of the brick or other covering of such spandrel 
beams, girders, or lintels. The covering thickness shall be measured from the 
extreme projection of the metal in every case. 

Beams, Girders and Trusses—Coverings of. (a) The metal beams, 
girders, and trusses of the interior structural parts of a building shall be covered 
by one of the fireproof materials hereinbefore specified, so applied as to be sup¬ 
ported entirely by the beam or girder protected, and shall be held in place by 
the support of the flaneres of such beams or girders and by the cement mortar 
used in setting. 

(b) If the covering is of brick, it shall be not less than four inches thick; 
if of hollow tiles or if of solid porous tiles or if of terra cotta, such tiles shall be 
not less than two inches thick, applied to the metal in a bed of cement mortar; 
hollow tiles shall be constructed in such a manner that there shall be one air 
.space of at least three-fourths of an inch by the width of the metal surface to be 
covered within such clay coverings; the minimum thickness of concrete on the 
bottom and sides of metal shall be two inches. 

(c) The top of all beams, girders, and trusses shall be protected with not 
less than two inches of concrete or one inch of burnt clay bedded solid on the 
metal in cement mortar. 

(d) In all cases of beams, girders, or trusses, in roofs or floors, the pro¬ 
tection of the bottom flanges of the beams and girders and as much of the web 
of the same as is not covered by the arches shall be made as hereinbefore specified 
for the covering of beams and girders. In every case the thickness of the cover¬ 
ing shall be measured from the extreme projection of the metal, and the entire 
space or spaces between the covering and the metal shall be filled solid with one 
of the fireproof materials, excepting the air spaces in hollow tile. 


STEEL CONSTRUCTION 


349 


(e) Provided, however, that all girders or trusses when supporting loads 
from more than one story shall be fireproofed with two thicknesses of fireproof 
material or a combination of two fireproof materials as required for exterior 
columns, and each covering of fireproof material shall be bedded solid in cement 
mortar. 

Fireproofing ofExteriorSidesof Mull ions. In buildings required by this 
chapter to be of fireproof construction on exposures where metal frames, doors, 
sash, and wire glass are not required, all vertical door or window mullions over 
eight inches wade shall be fa^ed with incombustible material, and horizontal 
transom bars over six inches wide shall be faced with a fireproof or with an incom¬ 
bustible material. 

********* 

Iron or Steel Plates for Support of Wall. Where iron or*steel plates or 
angles are used in each story for the support of the facings of the walls of such 
story, such plates or angles shall be of sufficient strength to carry the weight 
within the limits of fiber stress for iron and steel elsewhere specified in this 
chapter of the enveloping material for such story, and such plates or angles may 
extend to within two inches of the exterior of such covering. 


SPECIFICATIONS 

Purpose. The purpose of specifications is to give a detailed 
description of such features of the work as can thus be given more 
clearly or be more easily defined than on drawings. They must 
co-operate with and supplement the drawings, but should not repeat 
the data given on the drawings, for every repetition is an added 
opportunity for conflict or error. 

In addition to the technical requirements referred to above, 
the specifications usually include certain items more related to the 
business transaction between the purchaser and the contractor. 

The specifications prepared by the designer are to be used for 
the guidance of the contractor in estimating the value of the work, 
of the mill in rolling the steel, of the engineer in preparing working 
drawings, and of the fabricating shop in manufacturing the material. 
These purposes should be kept in mind in writing specifications. 

The relation of the specifications to the contract should be 
clearly understood. In all cases the specifications should be made 
a part of the contract and they are then just as binding as if written 
into the contract. This indicates the importance of having them 
correctly written. As far as practicable, items in the specifications 
should not be repeated in the contract and, on the other hand, items 
which belong in the contract should not be in the specifications, 
for such repetitions lead to conflicting or ambiguous provisions. 


350 


STEEL CONSTRUCTION 


GENERAL CHARACTERISTICS 


A number of proposed standard specifications for structural 
steel have been published. Usually their purpose is more for the 
guidance of the designer than of the contractor. Some of them 
cover both purposes quite fully. Such a one is “Revised General 
Specifications for Structural Work for Buildings’’ by C. C. Schneider, 
M. Am. Soc., C. E., published in the Transactions of the American 
Society of Civil Engineers, Vol. LIV, page 490. This is referred to 
as Schneider’s Specifications. It can be used in whole or in part 
in making up specifications for a particular work. It is published 
and for sale by the Engineering News Publishing Company, so that 
copies are readily available. Consequently, in using the specifi¬ 
cations, the parts desired need not be copied but can be referred to 
by subject and paragraph number. Considerable portions are 
quoted in the specifications given later. 

When such general specifications are used, they must be supple¬ 
mented to provide for the special requirements of the work and for 
the business features before mentioned. 

Outline for Specifications. Complete specifications should 
include the following subjects: 


Instructions to Bidders 
General Conditions 
Scope of Work 
Loads 

Unit Stresses 


Quality of Materials 
Details of Construction 
Workmanship 
Painting 
Inspection 
Erection 


Instructions to Bidders. This is entirely a business feature and 
may be made a separate document from the specifications. But if 
so, it should accompany the specifications which are sent to bidders. 
As the instructions may contain items which might later affect the 
interpretation of the contract, it is best that they be included in 
the specifications and thus, automatically, become a part of the 
contract. 

The instructions give the time and place for submitting bids, 
the price basis, and any other directions pertinent to the case in 
hand. Bidders may be required to state the length of time required 
by them, if this will be a consideration in letting the contract. 


STEEL CONSTRUCTION 


351 


General Conditions. The general conditions have no very 
direct relation to the technical requirements but are more clearly 
business features. They cover such items as bonds, liability insur¬ 
ance, watchman service, etc. 

Scope of Work. This section of the specifications is devoted to 
the particular work under consideration and should be most care¬ 
fully stated, for it governs the amounts of material and service to 
be furnished. The paragraphs should cover the following items: 

(a) Describe definitely the work included. If separate draw¬ 
ings are made for the structural steel and show completely all the 
material to be furnished, the work may be so described. But if 
the structural steel is shown on drawings with other materials, 
particularly ornamental or miscellaneous iron, then the description 
must be given in sufficient detail to make it perfectly clear. It must 
be understood that the term “structural steel’’ is not definite enough 
to be used without such a description as required above, for struc¬ 
tural shapes may be used in stair construction, for furring, for win¬ 
dow frames, and in other situations, when it is desirable that such 
items be furnished .by other contractors. Cast-iron pedestals for 
steel columns and cast-iron columns, if used, are usually included in 
the contract with the structural steel. 

(b) Identify the drawings involved by numbers and dates. 

(c) State the place of delivery if erection is not included, and 
specify by whom transportation charges are to be paid. 

(d) Give requirements as to working drawings. 

Loads. It is desirable that the loads used in making the design 
be given in the specifications or marked on the drawings. The 
latter method is preferable for special loads, such as machinery, 
tanks, storage space, etc. This information is needed in detailing 
connections, stiffeners, etc. It is not sufficient to say that con¬ 
nections shall develop the full strength of the member, for there may 
be situations when a concentrated load near the end of a beam may 
produce a stress at the connection greater than would be produced 
by a uniformly distributed load. 

Unit Stresses. The unit stresses concern the design of the 
structural steel more than they do the manufacture and construction 
of it. However, they are needed in making the working drawings 
and should be included in the specifications. Those given in Schnei- 


352 


STEEL CONSTRUCTION 


der’s Specifications should be used unless local building ordinances 
require other values. 

Quality of Material. The quality-of material to be used is dis¬ 
cussed at length on p. 42. The specifications of the American 
Society for Testing Materials are recommended for general use. 
They need not be written into the specifications, it being sufficient 
to state that the steel shall comply with the “Standard Specifications 
for Structural Steel for Buildings”, adopted by the American Society * 
for Testing Materials. Similarly, the quality of cast iron may be 
specified. 

In this section the kind and quality of paint should be given. 

Details of Construction. This section of the specifications is 
concerned with such items as connections, rivet spacing, etc. It is 
chiefly to guide the engineers and draftsmen in making working 
drawings. Design drawings should be consistent with its provisions. 

Schneider’s Specifications are recommended for this portion of 
the specifications. They may be used by reference, saying that the 
details of construction should conform to Schneider’s Specifications 
in so far as they apply to this work; or the specific paragraphs which 
do apply may be referred to by number. 

Workmanship. The specifications for workmanship govern the 
operations in the shop. Schneider’s Specifications are recom¬ 
mended and may be used the same as for construction details. 

Painting. This is well covered by Schneider’s Specifications, 
which may be used without modification unless some special pro¬ 
vision is to be inserted. 

Inspection and Tests. Schneider’s Specifications are used for 
this part of the work without change. 

Erection. The specifications for erection must deal with the 
specific job. However, some of its provisions are general. 

The conditions at the site, the relations to the other parts of the 
structure, order of procedure, storage available, etc., etc., must be 
written to suit each case. If the contract for erection is separate 
from the contract for furnishing the steel, the division between 
them must be clearly defined. This division is usually best made 
at the place where the material is delivered on board cars. 

Quality of workmanship of erection applies generally to all 
structures. 


STEEL CONSTRUCTION 


353 


EXAMPLE OF SPECIFICATIONS 

The following specifications accord with the preceding discus¬ 
sions and may be used as a guide in writing specifications for a par¬ 
ticular structure. 


SPECIFICATIONS 

for the 

Structural Steel and Iron 
for a 

(Kind of Building) 
for 

(Owner) 


Instructions to Bidders. Bids will be received for the struc¬ 
tural steel and iron work required for (kind of building) located at 

. Street, in the City of 

.for the (owner) 

in accordance with the following specifications and the plans des¬ 
cribed therein. 

Bids must be filed at the office of... 

Architect, on or before noon,. 19. 

Bidders shall state a lump sum which shall include furnishing, 
delivering, and erecting the structural steel and iron work and shall 
also include the cost of the bond, insurance, and watch service as 
required under general conditions. 

General Conditions. 

Ownership. The building is known as the.Build¬ 
ing and is owned by the.[a partnership (or 

corporation) existing under the laws of the State of.] 

Location. It is located at. 

Street in the City of.on lots.(give 

legal description). 

Bond. The contractor shall furnish surety bond in the penal 
sum of one-half the contract price, guaranteeing the fulfillment of 
















354 


STEEL CONSTRUCTION 


the terms of the contract. Said bond shall be in terms and with 
surety satisfactory to the Architect. 

Liability Insurance. The contractor shall protect the owner 
against loss due to any damage to property or injury to persons 
which may result from his operations. He shall provide adequate 
liability insurance in a company approved by the Architect. 

Patented Articles. The contractor shall protect the owner 
against any claim arising out of the use of any patented article, 
appliance, or method. 

Protection. The contractor shall provide such barricades, 
scaffolding, staging, and other means of protection as may be re¬ 
quired to comply with the state and municipal laws and to ade¬ 
quately safeguard property and persons. 

Watchmen. The contractor shall keep competent watchmen on 
the building day and night. 

Scope. [Give a general description similar to the following: 
The building is designed for office purposes with stores on the first 
and second floors. It is twenty stories high above street level with 
a basement and sub-basement below street level. The ground area 
occupied is approximately 100 feet by 1G2 feet.] 

Work Covered. The work to be done under the specifications is 
the furnishing and the erecting of the structural steel and iron work. 
The contractor shall make the working drawings, furnish and fabri¬ 
cate the material, pay all transportation charges, assemble the 
material in place in the building, rivet the connections, and furnish 
the materials and labor for shop and field painting. 

Materials Included. The structural steel and iron work 
consists of the following items: (To be changed to suit the 
case). 

Grillage Beams and Girders 
Cast-Iron Pedestals 

I-Beam Reinforcement in Retaining Walls 

Structural Steel Framework 

Cast-Iron Columns 

Detached Lintels 

Cornice Brackets 

Roofing Tees 

Steel Chimney 

All minor parts belonging to the above items 


STEEL CONSTRUCTION 


355 


It includes all the material of the above character shown in the 
structural plans of the building and, in addition, it includes the 
detached lintels over exterior windows which are shown on the 
architectural plans. 

Materials Not Included. The structural steel and iron work 
(to be changed to suit the case) does not include the angles, channels, 
and hangers of the suspended ceiling over the top story, the elevator 
sheave beams, the beams and channels for the stairs other than those 
shown on the framing plans, the marquise framing, the steel column 
guards and door guards in the shipping room, and other like items 
shown on the architectural plans. It does not include the rods for 
reinforced concrete work shown on the structural plans except cer¬ 
tain items which are definitely marked on the drawings to be fur¬ 
nished with the structural steel. 

Plans. The structural plans consist of drawings prepared by 

. Structural Engineer for 

.Architect, as follows: 

(Give list of drawings) 


The architectural plans prepared by. 

Architect, which show structural steel and iron work not given on 
the structural plans are drawings No... 

While making the working, drawings, the contractor shall con¬ 
sult all architectural drawings which may be supplied to him, for 
the purpose of discovering discrepancies, making necessary allow¬ 
ances for clearance, providing connections and supports for other 
materials, etc. 

When provision must be made for attaching other materials to 
the structural steel work, the contractor shall furnish the holes 
required. If the necessary data are not given on the structural or 
architectural drawings, he shall apply to the Architect for the data 
before completing the working drawings. This applies particularly 
to stone, terra cotta, concrete, miscellaneous iron, ornamental iron, 
furring (wood and steel), pipes, and conduits. 

Working Drawings. The contractor is required to prepare 
working drawings to supplement the ’design drawings prepared by 
the Engineer and the Architect. Two copies of such drawings shall 








356 


STEEL CONSTRUCTION 


be submitted to the Architect for approval. After approval, three 
copies shall be furnished to the Architect for his files, and as many 
copies as may be required shall be furnished to the inspector and to 
other trades. 

Copies or prints of drawings issued before approval shall be 
marked “Not Approved” and those issued after approval shall be 
marked “Approved Drawing.” During the preparation of the 
working drawings, the contractor shall examine the design drawings 
carefully for omissions and errors, and when such omissions and 
errors are discovered, he shall submit them to the Architect for 
correction. Figured dimensions only shall be used. 

If the contractor does not have a force of engineers competent 
to prepare working drawings to the satisfaction of the Architect, he 
shall employ a consulting engineer for that purpose. 

Working drawings shall be accompanied by erection diagrams 
and a complete index giving marking numbers of the material and 
page or sheet numbers of the drawings. 

Approval of Working Drawings. If the working drawings are 
found to be consistent with the design drawings and these specifica¬ 
tions, and if the details shown on them are satisfactory, they will be 
approved. One copy so marked will be returned to the contractor. 
If not consistent and satisfactory as above, one copy will be marked 
to indicate the required changes and returned to the contractor, 
who shall then make the required changes, and if so ordered, shall 
submit copies of revised drawings for final approval. 

The Architect’s approval will cover the arrangement of the 
principal members and auxiliary members, and the strength of con¬ 
nections. At the same time an effort will be made to discover any 
errors in sizes of material, in general dimensions, and in detail dimen¬ 
sions; but the responsibility for these items shall remain with the 
contractor. 

The manufacturing of any material or the performing of any 
work before approval of working drawings will be entirely at the 
risk of the contractor. 

Transportation. The contractor shall pay all costs of transpor¬ 
tation of material from his shop to the building site and shall assume 
all risk of loss and damage in transit. 

Loads. The structural steel and iron work is designed to sup- 


STEEL CONSTRUCTION 


357 


port the estimated dead loads and the assumed live loads. In 
making the working drawings, the contractor shall design all con¬ 
nections to carry the same loads. 

The dead loads are the actual weights of all materials of con¬ 
struction in the positions which they occupy, except that the effect 
of movable partitions may be assumed to be equivalent to a uni¬ 
formly distributed load of 25 pounds per square foot of floor on all 
office floors. On other floors and along corridors, the partitions 
shall be provided for where they occur. 

The live loads for which this structure is designed are: 


(Subject to change) 


Roof 

Office floor 
Second floor 
First floor 
Sidewalk 
Wagon space and 
shipping room 


•50 lb. per sq. ft. 
50 lb. per sq. ft. 
100 lb. per sq. ft. 
125 lb. per sq. ft. 
150 lb. per sq. ft. 

250 lb. per sq. ft. 


The special loads from elevators, tanks, etc., are marked on the 
drawings. 

The framework is designed for a wind pressure of 20 pounds per 
square foot applied horizontally to the vertical projection of the 
building in any direction. 

Where stresses are marked on the drawings, they may be used 

as the full effect of the loads. 

% 

Beams and girders shall have their connections made strong 
enough to develop the full capacity of the members when they are 
uniformly loaded, even when the live and dead loads are less than 

this capacity. 

Unit Stresses. The design is based on the unit stresses given 
in Schneider’s Specifications, * paragraphs 19 to 34 inclusive. These 
unit stresses shall be used in proportioning the details. 

Steel 

19. Permissible Strains. All parts of the structure shall be proportioned 
so that the sum of the dead and live loads, together with the impact, if any, 
shall not cause the strains to exceed those given in the following table: 

♦‘‘Revised Specifications for Structural Work for Buildings" by C. C. Schneider, M. Am. 
Soc. C. E., Trans. Am. Soc. C. E.,\ ol. LIV, Page 494. 



358 


STEEL CONSTRUCTION 


Pounds per 
square inch 


Tension, net section.16,000 

Direct compression.16,000 

Shear, on rivets and pins.12,000 

Shear, on bolts and field rivets. 9,000 

Shear, onqalate-girder web (gross section).10,000 

Bearing pressure, on pins and rivets. 24,000 

Bearing pressure, on bolts and field rivets.18,000 

Fiber strain, on pins. 24,000 


20. Permissible Compression Strains. For compression members, the 
permissible strain of 16,000 lb. per sq. in. shall be reduced by the following 
formula: 

p = 16,000 — 70- 

Where p = permissible working strain per square inch in compression; 

l = length of piece, in inches, from center to center of connections; 
r = least radius of gyration of the section, in inches. 

21 For wind bracing, and the combined strains due to wind and the 
other loading, the permissible working strains may be increased 25%, or to 
20,000 lb. for direct compression or tension. 

22. Provision for Eccentric Loading. In proportioning columns, provision 
must be made for eccentric loading. 

23. Expansion Rollers. The pressure per linear inch on expansion rollers 
shall not exceed 600 d, where d = diameter of rollers, in inches. 

2/,. Combined Strains. Members subject to the action of both axial and 
bending strains shall be proportioned so that the greatest fiber strain will not 
exceed the allowed limits for the axial tension or compression in that member. 

25. Reversal of Strains. Members subject to reversal of strains shall be 
proportioned for the strain giving the largest section, but their connections shall 
be proportioned for the sum of the strains. 

26. Net Sections. Net sections must be used in calculating tension mem¬ 
bers, and in deducting the rivet holes; they must be taken | in. larger than the 
nominal size of the rivets. 

27 Pin-connected riveted tension members shall have a net section 
through the pin holes 25% in excess of the net section of the body of the member. 
The net section back of the pin hole shall be at least 0.75 of the net section through 
the pin hole. 

28. Compression Members Limiting Length. No compression member 
shall have a length exceeding 125 times its least radius of gyration, except those 
for wind and lateral bracing, which may have a length not exceeding 150 times 
the least radius of gyration 

29. Plate Girders. Plate girders shall be proportioned on the assumption 
that one-eighth of the gross area of the web is available 'as flange area. The 
compression flange shall have at least the same sectional area as the tension 
flange, but the unsupported length of the flange shall not exceed 16 times its width. 

30. In plate girders used as crane runways, if the unsupported length of 
the compression flange exceeds 12 times its width, the flange shall be figured as 
a column between the points of support. 










STEEL CONSTRUCTION 


359 


81. Web Stiffeners. The web shall have stiffeners at the ends and inner 
edges of bearing plates, and at all points of concentrated loads, and also at 
intermediate points, when the thickness of the web is less than one-sixtieth of 
the unsupported distance between flange angles, generally not farther apart than 
the depth of the full web plate, with a minimum limit of 5 feet. 

82. Rolled Beams. I-beams, and channels used as beams or girders, shall 
be proportioned by their moments of inertia. 

88. Limiting Depth of Beams and Girders. The depth of rolled beams in 
floors shall be not less than one-twentieth of the span and, if used as roof purlins, 
not less than one-thirtieth of the span. 

In case of floors subject to shocks and vibrations, the depth of beams and 
girders shall be limited to one-fifteenth of the span. If shallower beams are 
used, the sectional area shall be increased until the maximum deflection is not 
greater than that of a beam having a depth of one-fifteenth of the span, but the 
depth of such beams shall in no case be less than one-twentieth of the span. 

Cast Iron 

Permissible Strains. Compression.12,000 lb. per sq. in. 

Tension... 2,500 “ “ “ “ 

Shear.,. 1,500 “ . 

Quality of Materials. Steel. The structural steel shapes, 
plates, and rivets shall conform to the Standard Specifications for 
Structural Steel for Buildings adopted by the American Society for 
Testing Materials*, as follows: 

SPECIFICATIONS FOR STRUCTURAL STEEL FOR BUILDINGS 

Structural steel may be made by either the open-hearth or Bessemer 

process. 

Rivet steel and plate or angle material over f inch thick, which is to be 
punched, shall be made by the open-hearth process.. 

The chemical and physical properties shall conform to the limits shown in 
the tabular matter on the following page. 

For the purposes of these specifications, the yield point shall be determined 
by the careful observation of the drop of the beam or halt in the gage of the 
testing machine. 

In order to determine if the material conforms to the chemical limitations 
prescribed ******* analysis shall be made by the manufacturer 
from a test ingot taken at the time of the pouring of each melt or blow of steel, 
and a correct copy of such analysis furnished to the engineer or his inspector. 

Specimens for tensile and bending tests shall be made by cutting coupons 
from the finished product, which shall have both faces rolled and both edges 
milled to the form shown by Fig. 1 (see Fig. 46); or with both edges parallel; or 
they may be turned to a diameter of f inch for a length of at least 9 inches, 
with enlarged ends. 

(a) For material more than | inch thick the bending test specimen may be 
1 inch by \ inch in section. 

( b ) Rivet rounds and small rolled bars shall be tested as rolled. 

•American Society for Testing Materials, Edgar Marburg, Secretary, University of Penn¬ 
sylvania, Philadelphia. 






360 STEEL CONSTRUCTION 

Properties of Structural Steel 


Properties Considered 

Structural Steel 

Rivet Steel. Open 
Heartn 

Phosphorus, max , Bessemer. ... 

0.10 per cent 

0.06 per cent 

Phosphorus, max., open hearth. 

0.06 per cent 

Ult. tensile strength, pounds per sq. in. . 

55,000-65,000 

48,000-58,000 

Yield point. .; ■. 

| Ult. tens. str. 

| Ult. tens. str. 

Elongation, min. per Cent in 8 in......... 

1,400,000 

Ult. tens. str. 

1.400,000 

Ult! tens. str. 

Character of fracture.. 

Silky' 

Silky 

Cold bend without fracture.. 

180° to diameter 
of 1 thickness 

180° flat 


Material which is to be used without annealing or further treatment shall 
be tested in the condition in which it comes from the rolls. When material is to 
be annealed or otherwise treated before use, the specimens for tensile tests, 
representing such material, shall be cut from properly annealed or similarly 
treated short lengths of the full section of the bar. 

At least one tensile and one bending test shall be made from each melt or 
blow of steel as rolled. In case steel differing f inch and more in thickness is 
rolled from one melt or blow, a test shall be made from the thickest and thinnest 
material rolled. , Should either of these test specimens develop flaws, or should 
the tensile test specimen break outside of the middle third of its gaged length, 
it may be discarded and another,test specimen substituted therefor. If tensile 
test specimen does not meet the specification, additional tests may be made. 

(c) The bending test may be made by pressure or by blows. 

For material less than A inch and more than f inch in thickness, the follow¬ 
ing modifications shall be made in the requirements for elongation. 

(d) For each increase of I inch in thickness above f inch, a deduction of 
1 shall be made from the specified percentage of elongation. 

(e) For each decrease of inch in thickness below inch, a deduction 
of 2 3 shall be made from the specified percentage of elongation. 

(/) For pins, the required percentage of elongation shall be 5 less than 
that specified ***** as determined on a test specimen, the center of 
which shall be 1 inch from the surface. 

Finished material must be free from injurious seams, flaws, or cracks, and 
have a workmanlike finish. 

Test specimens and every finished piece of steel shall be stamped with melt 
or blow number, except that small pieces may be shipped in bundles securely 
wired together, with the melt or blow number on a metal tag attached. 

A variation in cross section or weight of each piece of steel of more than 2\ 
per cent from that specified will be sufficient cause for rejection, except in case 
of sheared plates, which will be covered by the following permissible variations, 
which are to apply to single plates. 













STEEL CONSTRUCTION' 361 

When Ordered to Weight 

Plates 12% pounds per square foot or heavier: 

(q) Up to 100 inches wide, 2% per cent above or below the prescribed 
weight. 

(h) 100 inches wide and over, 5 per cent above or below. 

Plates under 12% pounds per square foot: 

(i) Up to 75 inches wide, 2 % per cent above or below. 

75 inches and up to 100 inches wide, 5 per cent above or 3 per cent, 
below. 

O’) 100 inches wide and over, 10 per cent above or 3 per cent below. 

When Ordered to Gage 

Plates will be accepted if they measure not more than 0.01 inch below the 
ordered thickness. 

An excess over the nominal weight corresponding to the dimensions on the 
order will be allowed for each plate, if not more than that shown in the following 
tables, one cubic inch of rolled steel being assumed to weigh 0.2833 pound. 

Plates j inch and over in thickness 


Thickness 

Ordered. 

Inches 

Nominal 
Weights 
Lb. per 
sq. ft. 

Width of Plate 

Up to 75 in. 

75 in. and up 
to 100 in. 

100 in. and 
up to 115 in. 

Over 115 in. 

1-4 
5-16 
3-8 
7-16 
1-2 
9-16 
5-8 
Over 5-8 

10.20 

12.75 

15.30 

17.85 

20.40 

22.95 

25.50 

10 per cent 

8 per cent 

7 per cent 

6 per cent 

5 per cent 

4 1 per cent 

4 per cent 

3 2 per cent 

14 per cent 
12 per cent 
10 per cent 

8 per cent 

7 per cent 
62 per cent 

6 per cent 

5 per cent 

18 per cent 
16 per cent 
13 per cent 
10 per cent. 

9 per cent 

81 per cent 

8 per cent 
62 per cent 

17 per cent 

13 per cent 

12 per cent 

11 per cent 

10 per cent 

9 per cent 


Plates under \ inch in thickness 


Thickness 

Ordered 

Inches 

Nominal 

Weights 

Lb. per sq. ft. 

Width of Plate 

Up to 50 in. 

50 in. and up 
to 70 in. 

Over 70 in. 

1-8 up to 5-32 
5-32 up to 3-16 
3-16 up to 1-4 

5.10 to 6.37 
6.37 to 7.65 
7.65 to 10.20 

10 per cent 

82 per cent 

7 per cent 

15 per cent 
12-2 per cent 

10 per cent 

20 per cent 

17 per cent 

15 per -cent 


The inspector representing the purchaser shall have all reasonable facilities 
afforded to him by the manufacturer to satisfy him that the finished material is 
furnished in accordance with these specifications. 

All tests and inspections shall be made at the place of manufacture, prior 
to shipment. 

Cast Iron. The cast iron shall conform to the Standard Speci¬ 
fications for Gray Iron Castings adopted by the American Society 
for Testing Materials*, as follows: 

♦American Society for Testing Materials, Edgar Marburg, Secretary, University of Penn¬ 
sylvania, Philadelphia. 



















362 


STEEL CONSTRUCTION 


SPECIFICATIONS FOR GRAY IRON CASTINGS 

Unless furnace iron is specified, all gray castings are understood to be 
made by the cupola process. 

The sulphur contents to be as follows: __ 

Light castings..not over 0.08 per cent 

Medium castings...not over 0.10 per cent 

Heavy casting. not over 0.12 per cent 

In dividing castings into light, medium, and heavy classes, the following 
Standards have been adopted: 

Castings having any section less than £-inch thick shall be known as light 
castings. 

Castings in which no section is less than 2 inches thick shall be known as 

heavy castings. 

Medium castings are those not included in the above classification. 

Transverse Test. The minimum breaking strength of the “Arbitration Bar” 
under transverse load shall not be under: 

Light castings......2,500 lb. 

Medium castings.2,900 lb. 

Heavy castings. ....... .....3,300 lb. 

In no case shall the deflection be under 0.10 inch. 

Tensile Test. Where specified, this shall not run less than; 

Light castings. 18,000 lb. per sq. in. 

Medium castings. .21,000 lb. per sq. in. 

Heavy castings. 24,000 lb. per sq. in. 

The quality of the iron going into castings under specification shall be 
determined by means of the “Arbitration Bar’’. This.is a bar 1 j inches in diam¬ 
eter and 15 inches long. It shall be prepared as stated further on and tested 
transversely. The tensile test is not recommended, but in case it is called for, 
the bar as shown in Fig. 1, (figure not given) and turned up from any of the 
broken pieces of the transverse test shall be used. The expense of the tensile 
test shall fall on the purchaser. 

Two sets of two bars shall be cast from each heat, one set from the first 
and the other set from the last iron going into the castings. Where the heat 
exceeds twenty tons, an additional set of two bars shall be cast for each twenty 
tons or fraction thereof above this amount. In case of a change of mixture 
during the heat, one set of two bars shall also be cast for every mixture 
other than the regular one. Each set of two bars is to go into a single mold. 
The bars shall not be rumbled or otherwise treated, being simply brushed off 
before testing. 

The transverse test shall be made on all the bars cast, with supports 12 
inches apart, load applied at the middle, and the deflection at rupture noted. 
One bar of every two of each set made must fulfil the requirements to permit 
acceptance of the castings represented. 

The mold for the bars is shown in Fig. 2 (figure not given.). The bottom 
of the bar is rs inch smaller in diameter than the top, to allow for draft and for 
the strain of pouring. .The pattern shall not be rapped before withdrawing. 
The flask is to be rammed up with green molding sand, a little damper than 











STEEL CONSTRUCTION 


363 


usual, well mixed and put through a No. 8 sieve, with a mixture of one to twelve 
bituminous facing The mold shall be rammed evenly and fairly hard, thor¬ 
oughly dried, and not cast until it is cold. The test bar shall not be removed 
from the mold until cold enough to be handled. 

The rate of application of the load shall be from 20 to 40 seconds for a 
deflection of 0.10 inch. 

Borings from the broken pieces of the “Arbitration Bar” shall be used for 
the sulphur determinations. One determination for each mold made shall be 
required. In case of dispute, the standards of the American Foundrymen’s 
Association shall be used for comparison. 

Castings shall be true to pattern, free from cracks, flaws, and excessive 
shrinkage. In other respects they shall conform to whatever points may be 
specially agreed upon. 

The inspector shall have reasonable facilities afforded him by the manu¬ 
facturer to satisfy him that the finished material is furnished in accordance with 
these specifications. All tests and inspections shall, as far as possible, be made 
at the place of manufacture prior to shipment. 

Paint. The paints used shall be red lead paint for the shop 
coat and graphite paint for the field coat. 

The red lead paint shall be made of red lead containing not less 
than 95 per cent Pb 3 0 4 , for the pigtnent and pure raw linseed oil 
with not more than 8 per cent of turpentine or Japan drier for the 
vehicle. 

The red lead paint shall be mixed on the premises where it is 
used, and each batch shall be used within twenty-four hours after 
being mixed. The mixing shall be done in a churn or other 
mechanical mixer. The material shall be used in the proportion 
of twenty-five pounds of red lead to one gallon of oil. 

The contractor shall furnish-samples of the lead and oil for 
testing, and if required to do so shall furnish the name-of the manu¬ 
facturer of the oil and of the dealers who have handled it. 

The graphite shall be the. 

brand manufactured by the.Company, 

or any other graphite paint of equal quality, if it is approved by the 
Architect. 

The contractor shall furnish samples of the graphite paint for 
analysis and test. He shall guarantee that the paint will fulfill all 
the published claims made for it by its manufacturer. 

Details of Construction. The details of construction shall coft- 
form to paragraphs 37 to 81, inclusive, of Schneider’s Specifications, 
in so far as their provisions are applicable to this work. 




364 


STEEL CONSTRUCTION 


37. Minimum Thickness of Material. No steel of less than \ in. thickness 
shall be used, except for lining or filling vacant spaces. 

38. Adjustable Members. Adjustable members in any part of structures 
shall preferably be avoided. 

39. Symmetrical Sections. Sections shall preferably be made symmetrical. 

40. Connections. The strength of connections shall be sufficient to 
develop the full strength ••of the member. 

41. No connection, except lattice bars, shall have less than two rivets. 

42. Floor Beams. Floor beams shall generally be rolled steel beams. 

43. For fireproof floors, they shall generally be tied with tie-rods at inter¬ 
vals not exceeding eight times the depth of the beams. This spacing may be 
increased for floors which are not of the arch type of construction. Holes for 
tie-rods, where the construction of the floor permits, shall be spaced about 3 in. 
above the bottom of the beam. 

44 • Beam Girder.- When more than one rolled beam is used to form a 
girder, they shall be connected by bolts and separators at intervals of not more 
than 5 ft. All beams having a depth of 12 in. and more shall have at least two 
bolts to each separator. 

45. Wall Ends of Beams and Girders. Wall ends of a sufficient number 
of joists and girders shall be anchored securely to impart rigidity to the structure. 

46. Wall Plates and Column Bases. Wall plates and columfi bases shall 

be constructed so that the load will be well distributed over the entire bearing. 
If they do not get the full bearing on the masonry, the deficiency shall be made 
good with.Portland cement mortar.* ' 

47. Floor Girders. The floor girders may be rolled beams or plate girders; 
they shall preferably be riveted or bolted to columns by means of connection 
angles. Shelf angles or other support may be provided for convenience during 
erection. 

48. Flange Plates. The flange plates of all girders shall be limited in width, 
so as not to extend, beyond the outer line of rivets connecting them to the angles, 
more than 6 in., or more than eight times the thickness of the thinnest plate. 

49. Web Stiffeners. Web stiffeners shall be in pairs, and shall have a close 
bearing against the flange angles. Those over the end bearing, or forming the 
connection between girder and column, shall be on fillers. Intermediate stiff¬ 
eners may be on fillers or crimped over the flange angles, The rivet pitch in 
stiffeners shall not be more than 5 in. 

60. Web Sfflices. Web plates of girders must be spliced at all points by 
a plate on each side of the web, capable of transmitting the full strain through 
splice rivets. 

61. Columns. Columns shall be designed so as to provide for effective 
connections of floor beams, girders, or brackets. 

They shall preferably be continuous over several stories. 

62. Column Splices. The splices shall be strong enough to resist the 
bending strain and make the columns practically continuous for their whole lengt h. 

63. Trusses. t Trusses shall preferably be riveted structures. Heavy 
trusses of long span, where the riveted field connections would become un¬ 
wieldy, or for other good reasons, may be designed as pin-connected structures. 

64 . Intersecting Members. Main members of trusses shall be designed so 
that the neutral axes of intersecting members shall meet in a common point. 


STEEL CONSTRUCTION 


365 


65. Roof Trusses. Roof trusses shall be braced in pairs in the plane of 
the chords. 

Purlins shall be made of shapes, or riveted-up plate, or lattice girders. 

Trussed purlins will not be allowed. 

66. Eyebars. The eyebars in pin-connected trusses composing a member 
shall be as nearly parallel to the axis of the truss as possible. 

67. Spacing of Rivets. The minimum distance between centers of rivet 
holes shall be three diameters of the rivet; but the distance shall preferably be 
not less than.3 in. for 1-in. rivets. 2* in. for 1-in. rivets, 21 in. for f-in. rivets, 
and If in. for f-in. rivets. 

68. For angles with two gage lines, with rivets staggered, the maximum 
in each line shall be twice as great as given in Paragraph 57, and, where two or 
more plates are used in contact, rivets not more than 12 in. apart in any direc¬ 
tion shall be used to hold the plates together. 

69. The pitch of the rivet, in the direction of the strain, shall not exceed 
6 in., nor 16 times the thinnest outside plate connected, and not more than 50 
times that thickness at right angles to the strain. 

60. Edge Distance. The minimum distance from the center of any rivet 
hole to a sheared edge shall be If in. for |-in. rivets, If in. for f-in. rivets, If in. 
for |-in. rivets, and 1 in. for f-in. rivets; and to a rolled edge, If, If, 1, and f-in., 
respectively. 

61. The maximum distance from any edge shall be eight times the thick¬ 
ness of the plate. 

62. Maximum Diameter. The diameter of the rivets in any angle carrying 
calculated strains shall not exceed one-quarter of the width of the leg in which 
they are driven. In minor parts, rivets may be | in. greater in diameter. 

63. Pitch at Ends. The pitch of rivets at the ends of built compression 
members shall not exceed four diameters of the rivets for a length equal to one 
and one-half times the maximum width of the member. 

64. Tie Plates. The open sides of compression members shall be provided 
with lattice having tie plates at each end at intermediate points where the 
lattice is interrupted. The tie plates shall be as near the ends as practicable. 
In main members, carrying calculated strains, the end tie plates shall have a 
length not less than the distance between the lines of rivets connecting them to 
the flanges, and intermediate ones not less than half this distance. , 

Their thickness shall be not less than one-fiftieth of the same distance. 

65. • Lattice. The thickness of lattice bars shall be not less than one-fortieth 
for single lattice and one-sixtieth for double lattice, of the distance between end 
rivets; their minimum width shall be as follows: 

For 15-in. channels, or built sectionsU, Jn ln rivets) 
with 3f and 4-in. angles.J 

For 12-, 10- and 9-in. channels, or built\ 2 i j n n. in rivets) 
sections with 3-in. angles.J 4 ' * 

For 8- and 7-in. channels, or built U }n /s_ in rivets) 
sections with 2f-in. angles.j 

For 6- and 5-in. channels, or builtj n (i_j n rivets) 
sections with 2-in. angles. J 4 

66. Lattice bars with two rivets shall generally be used in flanges more 
than 5 in. wide. 






366 


STEEL CONSTRUCTION 


67. Angle of Lallice. The inclination of lattice bars with the axis of the 
member, generally, shall be not less than 45°, and when the distance between 
the rivet lines in the flange is more than 15 in., if a single rivet bar is used, the 
lattice shall be double and riveted at t he intersection. 

68. Spacing of Lattice. The pitch of lattice connections, along the flange 
divided by the least radius of gyration of the member between connections, 
shall be less than the corresponding ratio of the member as a whole. 

69. Faced Joints. Abutting joints in compression members when faced 
for bearing shall be spliced sufficiently to hold the connecting members accur¬ 
ately in place. 

70. All other joints in riveted work, whether in tension or compression, 
shall be fully spliced 

71. Pin Plates. Pin holes shall be reinforced by plates where necessary; 
and at least one plate shall be as wide as the flange will allow; where angles are 
used, this plate shall be on the same side as t he angles. The plates shall contain 
sufficient rivets to distribute their portion of the pin pressure to the full cross 
section of the member 

72. Pins. Pins shall be long enough to insure a full bearing of all parts 
connected upon the turned-down body of the pin 

73. Members packed on pins shall be held against lateral movement. 

74. Bolls. Where members are connected by bolts, the body of these 
bolts shall be long enough to extend through the metal. A washer at least 
^ in thick shall be used under the nut. 

75. Fillers. Fillers between parts carrying strain shall have a sufficient 
number of independent rivets to transmit the strain to the member to which the 
filler is attached 

76. Temperature. Provision shall be made for expansion and contraction, 
corresponding to a variation of temperature of 150° Fahr.. where necessary. 

77. Rollers. Expansion rollers shall be not less than 4 in. in diameter. 

78. Slone Bolts Stone bolts shall extend not less than 4 in. into granite 
pedestals and 8 in. into other material. 

79. Anchorage. Columns which are strained in tension at their base shall 
be anchored to the foundations 

80. Anchor bolts shall be long enough to engage a mass of masonry, the 
weight of w r hich shall be one and one-half times the tension in the anchor 

81. Bracing. Lateral, longitudinal, and transverse bracing in all struc¬ 
tures shall preferably be composed of rigid members. 

Adjacent ends of column sections, which do not have full bear¬ 
ing, shall have bearing plates not less than § inch thick. 

Rivets generally shall be f inch in diameter, but the diameter of 
the rivet shall not be less than one-fourth of its grip; |-inch rivets 
shall be used when the pieces connected are f inch or more in thickness. 

No beam connections shall be less than the standards of the 
American Bridge Company. 

The clearance from the ends of beams to columns or to girders 
shall not exceed \ inch. 


STEEL CONSTRUCTION 


367 


Tie-rods between floor beams shall be threaded at both ends for 
a length of at least 3 inches. 

The number of rivets furnished for field connections shall be 
10 per cent in excess of the nominal number required. 

Chimney. The connections of the cast-iron or steel chimney to 
the framework shall be such as to permit expansion and contraction, 
due to changes in temperature. 

Provide flanges with holes for breeching connection. 

ch l m n evs may have either flanged joints or hub and 
spigot joints. The bearing surfaces shall have contact on the entire 
perimeter and shall be exactly at right angles to the axis of the pipe, 
being turned or planed, if necessary to make them so. The calking 
space in hub and spigot joints shall be filled with iron fillings and 
sal ammoniac and calked solid. Connections for anchors shall be 
cast on. 

Steel chimneys shall have lap joints for all shop connections. 
They may have either lap or flange joints for the field connections, 
except that the lap joints generally will be required for self-support¬ 
ing chimneys exposed to wind pressure. All joints shall be prac¬ 
tically air-tight and, if not so made by the riveting, shall be calked. 

Cast Iron. The ends of cast-iron columns and the tops of cast- 
iron base plates and pedestals shall be planed. 

Bolt holes in cast iron shall be drilled. Holes for grout may be 
cored. 

In each cast-iron pedestal a grout hole shall be provided which 
shall be not less than 2\ inches in diameter and placed as near the 
center of the base as practicable. Additional holes shall be provided 
in bases larger than 4 feet in diameter. 

The joints in cast-iron columns shall be made by means of 
flanges cast on the columns. Each joint shall be bolted with not 
less than four f-inch bolts. The metal in the flanges shall be not less 
than 1 inch thick. 

Unless otherwise designed, each beam connection shall consist 
of a bracket and a lug. The bracket shall sustain the entire reaction 
from the beam. It shall project not less than 4 inches from the 
column and shall slope g inch. The lug shall provide for two or 
more bolts connecting to the web of the beam. 


368 


STEEL - CONSTRUCTION 


Workmanship. The workmanship in the fabrication of the 
structural steel shall conform to paragraphs 23 to 51 of Schneider’s 
Specifications, in so far as they concern this work. 

23 General., All parts forming a structure shall be built in accordance 
with approved drawings The workmanship and finish shall be equal to the 
best practice in modern bridge work. 

24- Straightening Material Material shall be thoroughly straightened in 
the shop, by methods which will not injure It, before being laid off or worked in 
any way. 

25. Finish. Shearing shall be done neatly and accurately, and all por¬ 
tions of the work exposed to view shall be neatly finished 

26. Rivets. The size of rivets called for on the plans shall be understood 
to mean the actual size of the cold rivet before heating. 

27. Rivet Holes. The diameter of the punch for material not more than 
| in. thick shall be not more than in., nor that of the die more than | in. larger 
than the diameter of the rivet. Material more than | in thick, excepting in 
minor details, shall be sub-punched and reamed or drilled from the solid 

28. Punching. Punching shall be done accurately Slight inaccuracy in 
the matching of holes may be corrected with reamers. Drifting to enlarge 
unfair holes will not be allowed. Poor matching of holes will be cause for rejec¬ 
tion, at the option of the inspector 

29. Assembling. Riveted members shall have all parts well pinned up 
and firmly drawn together with bolts before riveting is commenced. Contact 
surfaces shall be painted (See Paragraph 52.) 

30. Lattice Bars. Lattice bars shall have neatly-rounded ends, unless 
otherwise called for. 

81. Web Stiffeners. Stiffeners shall fit neatly between the flanges of 
girders. Where tight fits are called for, the ends of the stiffeners shall be faced 
and shall be brought to a true contact bearing with the flange angles 

32. Splice Plates and Fillers. Web splice plates and fillers under stiffeners 
shall be cut to fit within 5 in. of flange angles 

33 Connection Angles. Connection angles for floor girders shall be flush 
with each other and correct as to position and length of girder. 

34- Riveting. Rivets shall be driven by pressure tools wherever possible. 
Pneumatic hammers shall be used in preference to hand driving 

35 Rivets. Rivets shall look neat and finished, with heads of approved 
shape, full, and of equal size. They shall be central on the shank and shall grip 
the assembled pieces firmly. Re-cupping and calking will not be allowed. 
Loose, burned, or otherwise defective rivets shall be cut out and replaced In 
cutting out rivets, great care shall be taken not to injure the adjoining metal. 
If necessary, they shall be drilled out. 

86. Field Bolts. Wherever bolts are used in place of rivets which trans¬ 
mit shear, such bolts must have a driving fit. A washer not less than J in. thick 
shall be used under the nut. 

37. Members to be Straight. The several pieces forming one built member 
shall be straight and shall fit closely together, and finished members shall be 
free from twists, bends, or open joints. 


STEEL CONSTRUCTION 


369 


38. Finish of Joints. Abutting joints shall-be cut or dressed true and 
straight and fitted closely together, especially where open to view. In compres¬ 
sion joints depending on contact bearing; the surfaces shall be truly faced, so as 
to have even bearings after they are riveted up complete and when perfectly 

aligned. 

39. Eyebars. Eyebars shall be straight and true to size, and shall be free 
from twists, folds in the neck or head, or any other defect. Heads shall be 
made by upsetting, rolling, or forging. Welding will not be allowed. The form 
of the heads will be determined by the dies in use at the works where the eyebars 
are made, if satisfactory to the engineer, but the manufacturer shall guarantee 
the bars to break in the body with a silky fracture, when tested to rupture. The 
thickness of the head and neck shall not vary more than ^ in. from the thickness 
of the bar. 

40. Boring Eyebars. Before, boring, each eyebar shall be perfectly an¬ 
nealed and carefully straightened. - Pin holes shall be in the center line of 
bars and in the center of heads.. Bars of the same length shall be bored so 
accurately that, when placed together, pins xj in. .smaller in diameter than the 
pin holes can be passed through the holes at .both ends of the bars at the same¬ 
time. 

41. Pin Holes. Pin holes shall be bored , true to gages, smooth and 
straight; at right angles to the'axis of the member, and parallel to each other, 
unless otherwise called for. • Wherever possible, the boring shall be done, after 
the member is riveted up. 

42. Variation in Pin. Holes, The distance from center to center of pin 
holes shall be correct within- X 2 in., and the diameter of the hole not more than 

in. larger than that of the pin, for pins up to 5 in. diameter, and xz in* for 

larger pins. 

43. Pins and Rollers. * Pins and rollers shall be turned accurately ,to 
gages, and shall be straight, smooth, and entirely free from flaws. 

44 . Pilot Nuts. At least one pilot and driving nut shall be furnished for 
each size of pin for each structure. 

45. Screw Threads. Screw threads shall make tight fits in the nuts, and 
shall be United States standard, except for diameters greater than If in., when 
they shall be made, with six threads per inch. 

46. Annealing. Steel, except in minor details, which has been partially 
heated shall be properly annealed. 

47. Steel Castings. All steel castings shall be annealed. 

48. Welds. Welds in steel will not be allowed. 

49. Bed Plates. Expansion bed plates shall be planed true and smooth. 
Cast wall plates shall be planed at top and bottom. The cut of the planing 
tool shall correspond with the direction of expansion. 

60. Shipping Details. Pins, nuts, bolts, rivets, and other small details 
shall be boxed or crated. 

61. Weight. The weight of every piece and box’shall be marked on it in 
plain figures. 

Curved framing, hoppers, bins, and other complicated work 
shall be assembled and fitted in the shop. 


370 


STEEL CONSTRUCTION 


Cast Iron. The ends of cast-iron columns and the tops of base 
plates and pedestals must be finished exactly at right angles to the 
vertical axis of the column. 

The thickness of metal in cast-iron columns shall be not less at 
any point than that marked on the design drawings. The inside 
must be concentric with the outside. Shifting of the core more than 
| inch will cause rejection. At least three holes shall be drilled in 
each column to test the thickness of metal. 

Fins, chaplets, and other irregularities shall be removed by 
chipping, leaving neatly-finished surfaces. • No holes shall be filled 
with cement or other substance, without permission from the Archi¬ 
tect. 

The best practice shall be followed in reference to the quality 
of sand, molding, and the stripping of molds from castings. 

Painting. The material shall be painted one coat of red lead 
paint at the shop and one coat of graphite paint after erection. 
The painting shall be done in accordance with paragraphs 52 to 58 
of Schneider’s Specifications. 

52. Shop Painting. Steelwork, before leaving the shop, shall be thor¬ 
oughly cleaned and given one good coating of pure linseed oil, or such paint as 
may be called for, well worked into all joints and open spaces. 

52. In riveted work, the surfaces coming in contact shall be painted 
before being riveted together. 

5\. Pieces and parts which are not accessible for painting after erection 
shall have two coats of paint before leaving the shop. 

55. Steelwork to be entirely embedded in concrete shall not be painted. 

56. Painting shall be done only when the surface of the metal is perfectly 
dry. It shall not be done in wet or freezing weather, unless protected under 
cover. 

57. Machine-finished surfaces shall be coated with white lead and tallow 
before shipment, or before being put out into the open air. 

58. Field Painting. After the structure is erected, the metal work shall 
be painted thoroughly and evenly with an additional coat of paint, mixed with 
pure linseed oil, of such quality and color as may be selected. The field paint 
shall be of different color from the shop paint. 

Inspection and Testing. The inspection and testing will be 
done by the Architect or his representative. The contractor shall 
furnish the facilities for inspecting and testing and be governed by 
all of the provisions contained in paragraphs 59 to 64 of Schneider’s 
Specifications. 

59. The manufacturer shall furnish all facilities for inspecting and testing 
the weight, quality of material, and workmanship. He shall furnish a suitable 


STEEL CONSTRUCTION 


371 


testing machine for testing the specimens, as well as prepare the pieces for the 
machine, free of cost. 

60. When an inspector is furnished by the purchaser, he shall have full 
access at all times to all parts of the works where material under his inspection 
is manufactured. 

61. The purchaser' shall be furnished with complete copies of mill orders, 
and no material shall be rolled and no work done before he has been notified as 
to where the orders have been placed, so that he may arrange for the inspection. 

62. The purchaser shall also be furnished w r ith complete shop plans, and 
must be notified well in advance of the start of the work in the shop, in order 
that he may have an inspector on hand to inspect the material and workmanship. 

63. Complete copies of shipping invoices shall be furnished to the pur¬ 
chaser with each shipment. 

64- If the inspector, through an oversight or otherwise, has accepted 
material or work which is defective or contrary to the specifications, this material, 
no matter in what stage of completion, may be rejected by the purchaser. 

Erection. Conditions at the Site. (To be changed to suit the 
case). The site of the building cannot be given over to the con¬ 
tractor for his exclusive use. He must conduct his work as directed 
by the Architect, and in harmony with the other contractors working 
on the building at the same time. 

There is no storage space on or adjacent to the building site so 
the contractor must deliver the material as needed for erection, 
except arrangements may be made from time to time for the tem¬ 
porary storage of small quantities of material. He shall provide 
elsewhere such storage space as he may need. 

Construction Equipment. The contractor shall furnish all 
equipment required for his operations. The equipment shall be ade¬ 
quate for its purpose, and must have ample capacity to carry on the 
work quickly and safely. The Architect shall have authority to order 
changes in equipment if, in his judgment, it is not adequate or safe. 

Storing. Stored materials must be placed on skids and not on 
the ground. They must be piled and blocked up so that they will 
not become bent or otherwise injured. 

Unpainted material shall hot be so stored in the open. The 
materials shall be handled with cranes or derricks as far as prac¬ 
ticable. They must not be dumped off of cars or wagons nor in any 
other way treated in a manner likely to cause injury. 

Erecting Steel and Iron Work. The structural steel and iron¬ 
work shall be erected as rapidly as the progress of the other work 
(particularly foundations and walls) will permit. 


372 


STEEL CONSTRUCTION 


Settmg Plates and Grouting. Base plates, l>earing plates, and 
ends of girders which require to be grouted, shall be supported 
exactly at proper level by means of steel wedges. The grout will 
be furnished and poured by the mason contractor. 

Plumbing , Leveling, Bracing. The structural steel and iron 
work shall be set accurately to the lines and levels established for 
the building, as shown on the drawings. Particular care shall be 
taken to have the work plumb and level before riveting. 

Necessary bracing shall be provided for this purpose, and for 
resisting stresses due to derricks and other erection equipment and 
erection operations. 

Elevator shafts shall be plumbed from top to bottom with 
piano wire and must be left perfectly plumb. 

Temporary Bolts. The members shall be connected tempor¬ 
arily with sufficient bolts to insure the safety of the structure until 
it is riveted. Not less than one-third the holes shall be bolted. 

Riveting. All field connections shall be riveted unless other¬ 
wise ordered. The riveting shall follow as closely as practicable 
after erection. The connecting members shall be drawn up tight 
with bolts before riveting. Rivets generally shall be driven with 
pneumatic hammers. 

The rivets must be of proper length to forip full heads. Rivets 
must be tight, with full concentric heads. Defective rivets must be 
cut out and re-driven. No re-cupping or calking will be allowed. 

Permanent Bolts. When bolts are used for permanent connec¬ 
tions, washers shall be placed under the nuts, the nuts drawn tight, 
and the threads checked. In such cases, bolts must be used which 
are provided for that purpose, and not ordinary machine bolts. 

Connections to cast iron shall be bolted. 

Removal of Equipment and Rubbish. The contractor shall 
remove the construction equipment as rapidly as its service is com¬ 
pleted and shall remove all rubbish from day to day. 

Immediately after final acceptance of the work, the contractor 
shall remove all his equipment and property and shall remove all 
rubbish resulting from his operations. 


INDEX 





INDEX 


PAQE 

A 

Angle connections......... 120 

Angles. 29 

B 

Beam.. 75 

restrained_ 75 

simple.._... 75 

Beam box girders. 159 

Beam design. 76 

deflection. 77, 80 

flexure... 77 

modulus of elasticity_.•_ 80 

shear.. 77, 79 

Beams 

anchors_ 134 

beam design, theory of_ 76 

bearings.. 130 

classification. 75 

connection of beams to beams_ 120 

angle connections_ 120 

special connections_ 124 

connections of beams to columns.. 124 

combination connections_ 127 

seat connect ions __ 124 

web connections__ 126 

construction details - 120 

definitions-- 75 

design of. practical illustration... 309 

details of construct ion_ 120 

lateral support- 112 

load effects, calculation of-- 80 

miscellaneous details-----. 134 

practical applications_ 113 

resistance, calculation of. 97 

sections- 76 

separators_ 127 

strength of, tables-100-107 

tie rods-----.— 129 

Bearing. 64 

Bearing plates---.130> 163 

Bending moment-- - 76 








































2 


INDEX 


PAGE 


Bending moment diagram 
restrained beam- 


unit bracing.-.263 

Bessemer process. 13 

Bethlehem columns.----189, 196-209 

tables.....-. 196 

Bolts.. 71 

bolts in tension......- 72 

machine bolts —. 72 

turned bolts. 72 

Breaking load. 47 


C 


Cantilevers...-.-. 

Cast iron. 

Cast-iron columns..—-- 

column sections.. 

details of__ 

method of design .. 

tables.. 

Cast-iron pedestals... 

Cement as a rust preventive.-- 

Center of gravity (C. G.). 

Channel columns, tables... 

Channels. 

Chemical composition of steel. 

Chimney supports.. 

Chord stress in girders... 

Column bases... 

cast-iron plates__ 

flat plates... 

steel grillage.. 

Column loads and their effects.... 

computation of loads.... 

concentric loads... 

eccentric loads.... 

illustration...... 

Column sections.... 

area... 

distance from neutral axis to extreme fiber 

moments of inertia... 

properties of... 

radius of gyration___ 

Columns.,.. 

Bethlehem _____ 

details of. 

brackets. 

connections ... 

lacing... 


.. 118 

. 51 

..225 

..226 

..232 

..226 

..229 

....220, 319 

..339 

.. 35 

_210-215 

.. 28 

.. 45 

..327 

..135 

....218, 319 

..220 

..219 

.224 

. 173 

. 173 

. 174 

_174, 315 

. 175 

183, 226, 318 

...._181 

. 181! 

.. 182 

. 181 

. 182 

. 173 

. 189 

.216 

.218 

.218 

.217 

















































INDEX 


3 


Columns 

details of 

riveting_ 

splices__ 

location of. 

practical illustration_ 

steel_ 

strength of. 

formulas_ 

unit stress.. 

tables__ 

wind bracing, stresses in 

Connections. 

beams to beams_ 

beams to column_ 

girders to columns_ 


PAOE 


.217 

.216 

..308 

.313 

.173 

_179,196-215, 229 

.179, 189, 229 

179, 189, 190, 192, 194 

. 196-209 

...266 

_ 120 

__120 

__ 124 

..166 


D 


Deflection....77, 80, 109 

Details of construction__—120, 134, 166, 231, 261, 263 

Dimensioning drawings-----329 


E 

Eccentric loads on columns- 

Elastic limit__-.— 

Equilibrium. 

Erection ..-. 


174, 227, 315 

. 47 

. 3 

.371 


F 


Factor of safety___ 

Fire, protection from-- 

Fireproof floor construction.. 

Fireproof materials-- 

Fireproofing--- 

requirements, Chicago Building Ordinances 

Floor construction, fireproof.. 

Floor framing, panel of--- 

Friction.... 


. 7 

.339 

.301, 306 

.342 

..294, 339 

.347 

.301, 306 

113, 303, 305, 306 
. 67 


G 

Girders (see Riveted girders). 

% 

H 


134 


H-sections.. 

Hangers (see Tension members) 


33 

233 



































4 


INDEX 


PAGE 


I 

I-beam with flange plates.. 

I-beams_ 

Inspection_ 

Inspection and tests... 


158 

25 

370 

48 


Joist 


J 


75, 81 


Lateral support. 172 

Lintel___75, 116 

Load effects, calculation of__ 137 

combined loads_ 89 

concentrated loads_•- 85 

cantilever beams_ 86 

simple beam_ 85 

simple beams on two supports and projecting at both ends_ 86 

typical loadings_ 93 

beam with two or more loadings_ 96 

moving loads_ 96 

simple loads.._ 93 

tabular data__ 93 

uniformly distributed loads__ 80 

cantilever beam___ l__81 

combination simple and cantilever beam_ 82 

joists_ 81 

Loads_295, 351, 356 

dead_295, 303, 304, 309 

live.........297, 299, 314 

v 

M 

Manufacture of steel- 9 

iron ore to pig iron. 9 

pig iron_ 10 

process of smelting_ 9 

pig iron to steel-•_ 11 

acid open-hearth process_ 14 

basic open-hearth process _ _ __ 16 

bessemer process_ 13 

rolling the ingots.... 18 

blooming..... _____ 19 

plate rolls_ 22 

roughing and finishing rolls_ 19 

Manufacture of steel sections_ 44 

Masonry..._'. 52 

Masonry supports. 327 










































INDEX 


5 


Material, quality of __ 

miscellaneous sections 

plates___ 

tees___ 

Mill and stock orders_ 

Miscellaneous properties 
Moment of inertia (I) .... 


PAGE 

.. 42 

.. 34 

.. 32 

. 31 

.. 40 

. 39 

36, 140, 182 


Neutral axis. 


N 


181 


O 

Open-hearth process_ 


14 


P 

Paint...335, 363 

Painting........ 335 , 370 

Pig iron. 10 

Plate box girders__ 160 

Plate girder (see Riveted girder)_ 134 

Plates_ 32 

Practical design of sixteen-story fireproof hotel. 269 

column pedestals_ 319 

column specifications_313 

dimensioning drawings_329 

fireproof specifications_ 294 

floor construction, type of. 301 

framing specifications_ 306 

loads. 295 

miscellaneo is features. 327 

wind bracing.. 322 

Price basis_ 40 

Protection (see Rust, Painting, and Fireproofing)- 333 

Punching- 62 


Q 


Quality of materials_ 352 

cast-iron_ 361 

paint- 363 

steel_359 


R 


Radius of gyration (r)-38, 182, 228 

Railway bridge grade steel.-.-.— 46 

Reaming..-.- 62 

Reduction of area- 48 

R eference books----- 5 







































6 


INDEX 


PAGE 


Resistance, calculation of- 97 

deflection.. 109 

deflection formulas_ 109 

safe span length- 110 

lateral support----.-...112 

resisting moment- 97 

application of tables to concentrated loads- 99 

section modulus_ 98 

tabular values for_98 

shearing resistance ____. 108 

Resisting moment---76, 77, 97, 135 

determination of_ 135 

chord stress method_ 135 

moment of inertia method_ 135 

Restrained beam_ 75 

Rivet tables-- 67 

Rivets_ 52 

bearing- 64 

driving-- 58 

hand riveting_.*--- 62 

•pneumatic hammer_ 61 

riveting machines in shop_ 60 

friction..-- 67 

function of______•_ 63 

investigation of riveted joints- 67 

length of.. 73 

ordinary sizes___>_•_.-a_»._•_ 52 

punching and reaming__ 62 

rivet heads___... > 56 

button head_._ 57 

flattened and countersunk head_ 57 

manufacture_ 57 

shear.. ... 65 

spacing- 53 

clearance_ 55 

edge distance__ 55 

gage. 54 

pitch_ 54 

tension__ 67 

Riveted girder. —..._.l....134 

beam box girder_ 159 

crane girder_ 164 

design, theory of ...—....135 

girder supporting a column.. 162 

I-beam with flange plates_ 158 

plate box girder. 160 

plate girder. 138 

plate girder lintel_ 164 

practical applications___ 162 



















































INDEX 


7 




Vi 


Ov 


f 


Riveted girder 

roof girder_______ 

unsymmetrical sections__. 1 .. 1.... 

Riveted girder design.. 

depth......,.. 

economy... 

flange section.. 

width of flange plates—....... 

with flange plates--- 

without flange plates__.___ 

length of flange plates....*-- 

graphical solution for concentrated loads... 

graphical solution for uniformly distributed loads__ 

moment of inertia required... 

rivets connecting flange angles to web...—.. 

number of rivets..---- 

rivet spacing computed from web bearing.--- 

rivet spacing in flanges..—.. 

riveting for cover plates-:--- 

spacing when load transmitted through flange rivets into web 

tables and diagrams........ 

thickness of web..... 

shearing value of web plates..... 

web stiffeners....-.. 

intermediate stiffeners —..... 

stiffeners at loaded points...... 

Riveted girder details..... 

connections to columns.... 

bracket connection---- 

web angle connection... 

end bearings....^.. 

lateral support..-.-.. 

splices.-.. 

Riveted joints---- 1 --- 

Riveters.-.-.. 

Riveting in girders.-. 

Rolling steel.-. 

Rust. 

cement as a preventive...-. 

paint as a preventive--- 


PAGE 


. 164 
. 160 
. 135 
. 138 
. 138 
. 141 
_ 143 
. 142 
. 141 
. 144 
. 145 
.. 145 
.. 140 
. 149 
_ 149 
. 152 
.. 150 
.. 150 
.. 152 
.. 154 
. 139 
.. 140 
146 
.. 148 
.. 146 
.. 165 
. 166 
. 167 
.. 166 
. 165 
. 172 
. 168 
. 67 
. 59 
. 149 
.. 18 

* 333 
_ 339 
.. 335 


Section modulus 



Section, steel—adaptability and use 


angles — 
channels . 
H-section 



39 

23 

29 

28 

33 














































8 


INDEX 


PAGE 


Section, steel—adaptability and use 

I-beams- 25 

Bethlehem sections_ 26 

Carnegie sections_ 26 

efficiency of minimum sections_ 27 

special sections- 25 

standard sections_ 25 

Shear_65, 77, 79, 108 

Simple beam_75, 81, 85 

Smelting_1- 9 

Span_ 75 

Spandrel_ 75 

Spandrel girders, practical illustration--310, 323, 328 

Specifications_- 349 

example of_353 

general characteristics-350 

purpose of_349 

details of construction_363 

erection_ 371 

example of_x-353 

general conditions_353 

inspection and testing-370 

loads_ 356 

outline_350 

painting_370 

quality of materials_359 

unit stresses_357 

workmanship_ 368 

Standard specifications_350 

bending requirements_ 44 

chemical analysis_ 43 

elongation and fracture_ 44 

process of manufacture_ 43 

range of application_ 43 

rivet steel strength__ 44 

tensile strength_ 43 

Strength of columns (see Tables)_ 189 

Structural steel_ 9 

manufacture of_ 9 

maximum allowable stresses on_ 51 

procedure in furnishing_ 8 

reliability of_ 42 

T 

Tables 

beams, strength of. ..100-107 

gages for angles__ 54 

moments of inertia of I-beams with holes in flanges_159 

safe loads for round cast-iron columns_ 229 















































INDEX 


9 


PAGE 

Tables 

safe loads on Bethlehem columns_196-209 

safe loads on channel columns_210-215 

typical loadings, reactions and bending moments for_ 94-95 

unit stress in compression_ 194 

unit stress in compression in columns_190-193 

Tables, use of_ 194 

Tank support_ 118 

Tees_ 31 

Tension members_233 

connection details_ 237 

definition and theory_•_ 233 

axial tension_233 

tension due to eccentricity_234 

net area_ 236 

sections_235 

Testing.-- 370 

U 

Unit stresses..-50, 51, 351, 357 

columns-179, 190, 192 

tension_ 234 

zees_ 30 

W 

Weights of materials_ 295 

Weight, variation in_ 41 

Wind__ .322, 329 

Wind bracing_ 1 _239, 322 

combined wind and gravity stresses in girders_ 262 

framework, systems of rectangular framework_ 246 

axial stresses_ 253 

triangular framew r ork_243 

horizontal pressures_239, 322 

moment diagram for a restrained beam- 262 

paths of stress_ 240 

wind bracing girders, design of_255, 323 

end connections for I-beam girders-261, 323 

end connections for riveted girders_255, 324 

wind stresses on columns, effect of----266, 322, 326 

Workmanship_368 

Y 

Yield point_ - 47 

Yield point and factor of safety—. 48 

Z 

30 


Zees 











































* 



t 




V 


'My; ^ 

-■ A ; Ai 




if'’A.: ' ' j 



"V 











